Barla G, Barla M Continuum and discontinuum modelling in tunnel engineering. Rudarsko-Geolosko-Naftni Zbornik Google Scholar. In: Keynote Lecture, Int. Bolla A, Paronuzzi P Numerical investigation of the pre-collapse behavior and internal damage of an unstable rock slope. Chen G, Huang R, Zhang F et al Evaluation of the possible slip surface of a highly heterogeneous rock slope using dynamic reduction method. A scheme to detect and represent contacts in a system composed of many polyhedral blocks.
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As indicated in the strength histogram, a proper tensile strength of the rock sample in the Brazilian test can be obtained by the splitting simulation, and the tensile strength of isotropic rock sample is slightly larger than that of horizontal foliation rock sample. To comprehensively analyze the fracture mechanism of anisotropic rock, the strengthening scheme of Section 3. As the foliation angles continue to increase, the orientation of main crack will be closer to the vertical central axis.
Meanwhile, the rock sample is crushed in the area between two foliations. To analyze the effect of foliation angles on the rock tensile strength, the failure strengths of anisotropic rock under two simulation schemes were compared, as shown in Figure 5. For the rock samples with different foliation angles, the failure strengths with a strengthening scheme are entirely larger than those without a strengthening scheme. As indicated in the trend line of Figure 5 , studies indicate that the failure strengths of rock with different foliation angles decrease as the foliation angle increases [ 25 , 26 ].
Figure 5 of Section 3. Therefore, for the splitting of vertical foliation rock, the simulations without a strengthening scheme were conducted, and the effect of foliation thickness in sample middle were also considered, as shown in Figure 6. As the foliation thickness is 0. However, as the foliation thickness is 0.
Moreover, the crushing degree near the sample loading positions also decreases. In summary, the effects of different rock foliation angles on the fracture forms and failure strengths of rock samples are significant. For the fracturing simulation of anisotropic rock in the Brazilian test, the splitting process of horizontal foliation rock can be well simulated by a strengthening scheme.
The strengthening scheme is also suitable for investigating the fracturing of rock samples with the smaller foliation angle; however, simulations without a strengthening scheme are more suitable for investigating the fracturing of rock samples with the larger foliation angle. Furtherly, the fracturing of the rock sample with vertical foliations can be well simulated by adjusting the foliation thickness of sample middle.
Under different strength parameters, the tensile failure strengths of the rock sample in the splitting simulation produce significant differences, as shown in Figure 7. As the foliation strengths increase, the failure strengths of the rock sample increase. Moreover, the tensile failure strength of the rock sample also increases with an increase of rock matrix strength. As the results of the splitting simulation, the tensile failure strengths of rock samples only change from 2.
This indicates the effect of matrix strength variation on the tensile strength of the rock sample is not obvious; however, the foliation strength variation significantly affects the tensile strength of the rock sample. To verify the simulation results, the current works are compared with [ 25 , 26 ], as shown in Figure 8.
In general, the fracture patterns of foliation rock in current simulation are consistent with those of laboratory tests. As the foliation angle increases, the cracks of rock samples mainly propagate along rock foliations. Meanwhile, there is a short horizontal crack in the lower part of the rock sample in current work, and there is also a crack along the foliation of rock sample in [ 26 ].
In this study, the fracturing processes of isotropic and anisotropic rock samples in the Brazilian test were simulated, and simulation results are consistent with the experiment results. The fracture mechanism of the rock sample in the Brazilian test can be well depicted by the continuum-discontinuum element method.
In Brazilian splitting test, the vertical load firstly applies to the rock matrix near the sample loading positions, and then, the vertical load gradually translates into the sample middle. For the isotropic and horizontal foliation rock in the splitting simulation of Brazilian test, the failure tensile strengths of rock samples are larger than those of the inclined and vertical foliation rock, so the isotropic and horizontal foliation rock samples relatively easily generate the compression-shear fracture and the integral tensile fracture.
During the stiff wire loading, the stress concentration near the loading positions easily causes the local failure of the rock sample, and the tensile strength obtained by splitting simulation is smaller than the actual tension strength of rock materials. Therefore, for the isotropic and horizontal foliation rock, a local strengthening scheme should be adopted to simulate the splitting of rock samples, which can simulate the integral tensile fracture and obtain the proper tension strength of the rock sample in the Brazilian test.
This indicates as the foliation angle is smaller, the stress concentration and rock foliation both affect the splitting results of the rock sample. This indicates the effect of larger angle foliations on sample splitting is larger than the rock matrix. The fracturing of vertical foliation rock can be well simulated by adjusting the foliation thickness of sample middle, which can be because, in the complex geological processes, the geometric widthess of rock foliation appears to be very small; however, the influence area of the weak layer structure on the rock sample may be much larger than that of its geometric size.
With the strength parameter variation of the rock foliation and matrix, the weak layer structures have a significant influence on the fracture form and failure strength of anisotropic rock, although rock matrix strengths are much higher than foliation strengths. Therefore, the adjustment of rock matrix strength cannot obviously change the tensile failure strength of the numerical sample, while the variation in the foliation strength can significantly affect the tensile failure strength of the rock sample.
The authors declare that they have no conflicts of interest to report regarding the present study. The authors gratefully acknowledge Dr. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles.
Journal overview. Special Issues. Academic Editor: Adolfo Preciado. Received 28 Apr Accepted 26 Jun Published 07 Jul Abstract In this study, the continuum-discontinuum element method CDEM was used to investigate the tensile fracture mechanism of rock materials.
Introduction Because the fracture resistance of rock material is weaker under tension than under compression, so the investigation of rock tensile fracturing is important. Simulation Program 2. Simulation Method In this paper, a coupling method of particle-block element based on the continuum-discontinuum element method CDEM is used to investigate the tensile fracture mechanism of rock materials.
Figure 1. Figure 2. Table 1. Figure 3. Splitting simulation of isotropic and horizontal foliation rock. Figure 4. Fracturing simulation of rock with different foliation angles. Figure 5. The relationship between foliation angle and failure strength. Figure 6. Figure 7. Failure strengths of rock samples with different foliation and matrix strengths.
Figure 8. References C. Chen, E. Pan, and B. Wang, W. Li, and H. Li, Y. Cheng, and X. Barla and L. View at: Google Scholar H. Niandou, J. Shao, J. Henry, and D. Cho, H. Kim, S. Jeon, and K. Debecker and A. Meier, E. Rybacki, T. Backers, and G. Tavallali and A. Park and K. Kuila, D. Dewhurst, A. Siggins, and M. Steen, A. Vervoort, and J. Cho, Y. Ogata, and K.
Hao and H. Khosravani, M. Silani, and K. Potyondy and P. Cho, C. Martin, and D.
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