• Computers and Concrete
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• v.20 no.4
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• pp.429-437
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• 2017

In this study, the effect of the tensile strength and ratio of disc spacing to penetration depth on the efficiency of tunnel boring machine (TBM) is investigated using Particle flow code (PFC) in two dimensions. Models with dimensions of $150{\times}70mm$ made of rocks with four different tensile strength values of 5 MPa, 10 MPa, 15 MPa and 20 MPa were separately analyzed and two "U" shape cutters with width of 10 mm were penetrated into the rock model by velocity rate of 0.1 mm/s. The spacing between cutters was also varied in this study. Failure patterns for 5 different penetration depths of 3 mm, 4 mm, 5 mm, 6 mm, and 7 mm were registered. Totally 100 indentation test were performed to study the optimal tool-rock interaction. An equation relating mechanical rock properties with geometric characteristics for the optimal TBM performance is proposed. The results of numerical simulations show that the effective rock-cutting condition corresponding to the minimum specific energy can be estimated by an optimized disc spacing to penetration depth, which, in fact, is found to be proportional to the rock's tensile strength.

• Advances in concrete construction
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• v.7 no.4
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• pp.241-247
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• 2019

In this paper the effect of bedding layer on the failure mechanism of rock in direct shear test has been investigated using particle flow code, PFC. For this purpose, firstly calibration of pfc2d was performed using Brazilian tensile strength. Secondly direct shear test consisting bedding layer was simulated numerically. Thickness of layers was 10 mm and rock bridge length was 10 mm, 40 mm and 60 mm. In each rock bridge length, bedding layer angles changes from $0^{\circ}$ to $90^{\circ}$ with increment of $15^{\circ}$. Totally 21 models were simulated and tested. The results show that two types of cracks develop within the model. Shear cracks and tensile cracks. Also failure pattern is affected by bridge length while shear strength is controlled by failure pattern. It's to be noted that bedding layer has not any effect on the failure pattern because the layer interface strength is too high.

• Computers and Concrete
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• v.31 no.1
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• pp.71-84
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• 2023

In this paper, the effects of the thickness of cubic samples on the tensile strength of concrete blocks were studied using experimental tests in the laboratory and numerical simulation by the particle flow code in three dimensions (PFC3D). Firstly, the physical concrete blocks with dimensions of 150 mm×190 mm (width×height) were prepared. Then, three specimens for each of seven different samples with various thicknesses were built in the laboratory. Simultaneously with the experimental tests, their numerical simulations were performed with PFC3D models. The widths, heights, and thicknesses of the numerical models were the same as those of the experimental samples. These samples were tested with a new tensile testing apparatus. The loading rate was kept at 1 kg/sec during the testing operation. Based on these analyses, it is concluded that when the thickness was less than 5 cm, the tensile strength decreased by increasing the sample thickness. On the other hand, the tensile strength was nearly constant when the sample thickness was raised to more than 5 cm (which can be regarded as a threshold limit for the specimens' thickness). The numerical outputs were similar to the experimental results, demonstrating the validity of the present analyses.

• Computers and Concrete
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• v.33 no.6
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• pp.659-670
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• 2024

The mechanical behaviour of layered concrete samples containing an internal crack was numerically studied by modelling the geo-mechanical specimens in the particle flow code in two dimensions (PFC2D). The numerical modelling software was calibrated with the experimental results of the Brazilian tensile strengths gained from the laboratory disc-type specimens. Then, the samples with the bedding layers and internal notch were numerically simulated with PFC2D under uniaxial compressive loading. In each specimen, the layers' thickness was 10 mm but the layer's inclination angle was changed to 0°, 30°, 60°, 90°, 120° and 150°. Of course, the layers'interfaces are considered to have very low strengths. The internal notch was kept at 3 cm in length however, its inclination angle was changed to 0°, 40°, 60° and 90°. Therefore, a total, of 24 numerical models were made to study the failure mechanism of the layered concrete samples. Considering these results, it has been concluded that the inclination angles of both internal crack and bedding layers affect the failure mechanism and uniaxial compressive strength of the concrete.

• Journal of Korean Tunnelling and Underground Space Association
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• v.8 no.3
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• pp.205-217
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• 2006

Rock and discontinuities are main factors consisting of a rock mass and the physical properties of each factor have direct effects on the mechanical stability of artificial structures in the rock mass. Because physical properties of the rock and discontinuities change a lot according to the size of test materials, a close attention is needed when the physical properties, obtained from laboratory tests, are used for the design of field structures. In this study, change of physical properties of intact materials due to the change of their size are studied. Six kinds of artificial materials including crystal, instead of an intact rock, are adopted for the study to guarantee the homogeneity of specimen materials even with relatively large size. Uniaxial strength and Young's modulus of each artificial material are checked out for a size effect and compared with the predicted values by Buckingham's theorem - dimensional analysis. A numerical analysis using PFC (Particle Flow Code) is also applied and primary factors influencing on the size effect are investigated.

• Structural Engineering and Mechanics
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• v.86 no.5
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• pp.607-619
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• 2023

This study, it was tried to evaluate the asphalt behavior under tensile loading conditions through indirect Brazilian and direct tensile tests, experimentally and numerically. This paper is important from two points of view. The first one, a new test method was developed for the determination of the direct tensile strength of asphalt and its difference was obtained from the indirect test method. The second one, the effects of particle size and loading rate have been cleared on the tensile fracture mechanism. The experimental direct tensile strength of the asphalt specimens was measured in the laboratory using the compression-to-tensile load converting (CTLC) device. Some special types of asphalt specimens were prepared in the form of slabs with a central hole. The CTLC device is then equipped with this specimen and placed in the universal testing machine. Then, the direct tensile strength of asphalt specimens with different sizes of ingredients can be measured at different loading rates in the laboratory. The particle flow code (PFC) was used to numerically simulate the direct tensile strength test of asphalt samples. This numerical modeling technique is based on the versatile discrete element method (DEM). Three different particle diameters were chosen and were tested under three different loading rates. The results show that when the loading rate was 0.016 mm/sec, two tensile cracks were initiated from the left and right of the hole and propagated perpendicular to the loading axis till coalescence to the model boundary. When the loading rate was 0.032 mm/sec, two tensile cracks were initiated from the left and right of the hole and propagated perpendicular to the loading axis. The branching occurs in these cracks. This shows that the crack propagation is under quasi-static conditions. When the loading rate was 0.064 mm/sec, mixed tensile and shear cracks were initiated below the loading walls and branching occurred in these cracks. This shows that the crack propagation is under dynamic conditions. The loading rate increases and the tensile strength increases. Because all defects mobilized under a low loading rate and this led to decreasing the tensile strength. The experimental results for the direct tensile strengths of asphalt specimens of different ingredients were in good accordance with their corresponding results approximated by DEM software.

• Journal of Korean Tunnelling and Underground Space Association
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• v.12 no.1
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• pp.31-41
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• 2010

This paper presents both numerical and physical modeling approaches for the dilation and spalling of rock recognized as typical process of rock around an underground opening at depth. For physical approach, laboratory testing of rectangular beams using a synthetic rock was used to investigate the onset of dilation and spalling. The beams are axially compressed and subjected to 4-point bending to provide non-uniform compressive stresses which are similar to the maximum tangential stress distribution around circular openings. Discrete element numerical analyses using commercial code $PFC^{2D}$ (Particle Flow Code) were performed to evaluate the stress path at various locations in the beams. The findings from these approaches suggest that the onset of dilation in laboratory tests appears to be a good indicator for assessing the stress magnitudes required to initiate spalling.

• Explosives and Blasting
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• v.22 no.1
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• pp.33-43
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• 2004

In this study, a comparison was made between the resulting behaviors of scaled model test and particle flow analysis for blasting demolition of a reinforced concrete structure. For the test and analysis, a progressive failure of a five-story structure was considered. The dimension analysis was carried out to properly scale down the real structure into the laboratory size. The test model was made of the mixture of gypsum, sand and water along with soldering lead to analogy reinforcing steel bars. The ratio of mixing components was chosen to best represent the scaled down strength and deformation modulus. The columns and girders of the structure were precasted in the laboratory and assembled right before the blasting test. The numerical analysis of the blasting demolition was carried out using PFC2D (Particle Flow Analysis 2-Dimension by Itasca). The results of the blasting of concrete lahmen structure showed roughly identical demolition behavior between scaled model test and numerical test. For the blasting of the reinforced concrete structure, the results were more identical and closer to the real demolition behavior, since the demolition behavior was better represented in this case due to the increased tensile strength of the component.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.337-351
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• 2023

In this paper, the shear behavior of soft filling in rectangular-hollow concrete specimens was simulated using the 2D particle flow code (PFC2D). The laboratory-measured properties were used to calibrate some PFC2D micro-properties for modeling the behavior of geo-materials. The dimensions of prepared and modeled samples were 100 mm×100 mm. Some disc type narrow bands were removed from the central part of the model and different lengths of bridge areas (i.e., the distance between internal tips of two joints) with lengths of 30 mm, 50 mm, and 70 mm were produced. Then, the middle of the rectangular hollow was filled with cement material. Three filling sizes with dimensions of 5 mm×5 mm, 10 mm×5 mm, and 15 mm×5 mm were provided for different modeled samples. The parallel bond model was used to calibrate and re-produce these modeled specimens. Therefore, totally, 9 different types of samples were designed for the shear tests in PFC2D. The shear load was gradually applied to the model under a constant loading condition of 3 MPa (σc/3). The loading was continued till shear failure occur in the modeled concrete specimens. It has been shown that both tensile and shear cracks may occur in the fillings. The shear cracks mainly initiated from the crack (joint) tips and coalesced with another one. The shear displacements and shear strengths were both increased as the filling dimensions increased (for the case of a bridge area with a particular fixed length).

• 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.