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RESEARCH PROGRESS ON PFC2D SIMULATION OF CRACK PROPAGATION CHARACTERISTICS OF CRACKED ROCK
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摘要: 二维颗粒流数值模拟（PFC2D）是目前研究裂隙岩石裂纹扩展特征的重要手段。在大量已有相关研究文献的基础上做了以下分析和总结：从颗粒接触本构模型、细观参数的标定和裂隙模拟方法3个方面对当前PFC2D的主要模拟方法进行了总结；根据PFC2D模拟裂隙岩石裂纹扩展特征的研究现状，重点对单裂隙、断续双裂隙岩石在不同加载方式下的裂纹扩展特征进行了深入总结。在此基础上，指出当前研究中存在如下不足：裂隙岩石的PFC2D模型未考虑断裂韧度是否符合实际、平行黏结模型模拟结果与室内试验结果存在差异、模拟裂隙与真实裂隙存在差异。结合研究中存在的不足，提出了相应的解决办法并进行展望，以期有助于裂隙岩石PFC2D模拟方法的发展。Abstract: Two dimensional numerical particle flow code(PFC2D) is an important method to study the crack propagation characteristics of cracked rock. In review of related literatures, it is analyzed and summarized as follows:the current PFC2D simulation methods are summarized in three aspects of particle contact constitutive model, microparameters calibration and simulation method of crack. According to the current research, the PFC2D simulation of crack propagation characteristics is summarized focusing on the single cracked, intermittent double cracked rock under different loading methods. On this basis, the shortcomings of the current research are pointed out as follows. The fracture toughness of PFC2D model is not in line with the actual value of rock. Simulation results of parallel-bond model and test results of rock are different. There are differences between real crack and simulation crack. Combined with the existing shortcomings in the study, the corresponding solutions are put forward and are expected to contribute to the development of PFC2D simulation methods for cracked rocks.
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Key words:
- PFC2D /
- Cracked rock /
- Crack propagation /
- Research progress
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图 1 平直节理接触模型(Potyondy，2012)
Figure 1. Flat-jointed contact model(Potyondy, 2012)
图 2 PFC2D中裂隙的模拟方法(陈鹏宇，2015)
a.采用JSET命令模拟裂隙；b.采用一定厚度的颗粒模拟充填裂隙；c.删除一定厚度颗粒模拟裂缝；d.采用光滑节理模型模拟裂隙
Figure 2. Simulation methods of crack in PFC2D(Chen, 2015)
图 3 单轴压缩条件下裂纹扩展方式(蒋明镜等，2012)
Figure 3. Propagation of a crack subjected to uniaxial compression(Jiang et al., 2012)
图 4 裂隙岩石(裂隙倾角90°)的试验结果和模拟结果
a.试验结果；b. Lee et al.(2011)的模拟结果；c.刘华伟等(2016)的模拟结果；d.本文模拟结果
Figure 4. Laboratory test and PFC2D simulation results of cracked rock(crack dip is 90°)
图 5 裂隙岩石(裂隙倾角60°)的试验结果和模拟结果
a.试验结果；b. Lee et al.(2011)的模拟结果；c.黄达等(2013 a)的模拟结果；d.本文模拟结果
Figure 5. Laboratory test and PFC2D simulation results of cracked rock(crack dip is 60°)
图 6 非闭合裂隙岩石的PFC2D模拟结果
a.裂隙倾角0°；b.裂隙倾角30°；c.裂隙倾角60°；d.裂隙倾角90°
Figure 6. PFC2D simulation results of non-closed cracked rock
图 7 闭合裂隙岩石的PFC2D模拟结果
a.裂隙倾角0°；b.裂隙倾角30°；c.裂隙倾角60°；d.裂隙倾角90°
Figure 7. PFC2D simulation results of closed cracked rock
图 8 裂隙倾角与岩石单轴压缩强度的关系曲线
Figure 8. Relationship between crack dip and uniaxial compression strength of rock
表 1 砂岩宏观参数试验值和模拟值
Table 1. Tested and simulated macroscopic parameters of sandstone
试样 E50
/GPav σf
/MPaσt
/MPaKIC
/MPa·m1/2Kimachi砂岩 13.2 0.18 66.9 4.9 0.589 数值试样(平直节理模型) 13.1 0.17 66.8 5.0 0.552 数值试样(平行黏结模型) 13.0 0.19 67.4 16.3 3.562 
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Bobet A, Einstein H H. 1998. Fracture coalescence in rock-type material under uniaxial and biaxial compressions[J]. International Journal of Rock Mechanics and Mining Sciences, 35 (7):863-888. doi: 10.1016/S0148-9062(98)00005-9 Cen D F, Huang D. 2014a. Mesoscopic displacement modes of crack propagation of rock mass under uniaxial compression with high strain rate[J]. Journal of China Coal Society, 39 (3):436-444. Cen D F, Huang D, Huang R Q. 2014b. Step-path failure mode and stability calculation of jointed rock slopes[J]. Chinese Journal of Geotechnical Engineering, 36 (4):695-706. Cen D F. 2013. Modeling of step-path failure mechanism in rock slopes using PFC2D and evaluating on its stability[D]. Chongqing: Chongqing University. Chen F. 2002. The theoretical and experimental investigation on rock fracture due to shear-compression loading[D]. Changsha: Central South University. Chen P Y, Yu H M. 2016. Relationship between macroparameters and microparameters of flat-jointed bonded-particle material and calibration of microparameters[J]. Journal of Civil, Architectural & Environmental Engineering, 38 (5):74-83. https://www.researchgate.net/publication/311260838_Relationship_between_macroparameters_and_microparameters_of_flat-jointed_bonded-particle_material_and_calibration_of_microparameters Chen P Y. 2015. Characteristics Analysis of Slope Structure and Stability Study on High Rock Slope: a Case Study of the High Rock Slopes in Longsi Mine, Jiaozuo City[D]. Wuhan: China University of Geosciences. Chen P Y. 2017. Effects of microparameters on macroparameters of flat-jointed bonded-particle materials and suggestions on trial-and -error method[J]. Geotechnical and Geological Engineering, 35 (2):663-677. doi: 10.1007/s10706-016-0132-5 Chen X Y. 2015. Effect of Single closed central fissure on failure characteristics of cracked rock under uniaxial compression[J]. Journal of Yangtze River Scientific Research Institute, 32 (9):104-110. Cho N, Martin C D, Sego D C. 2007. A clumped particle model for rock[J]. International Journal of Rock Mechanics and Mining Sciences, 44 (7):997-1010. doi: 10.1016/j.ijrmms.2007.02.002 Cundall P A, Strack O D L. 1979. A discrete numerical model for granular assemblies[J]. Géotechnique, 29 (1):47-65. doi: 10.1680/geot.1979.29.1.47 Deng H F, Zhu M, Li J L, et al. 2012. Study of mode-Ⅰ fracture toughness and its correlation with strength parameters of sandstone[J]. Rock and Soil Mechanics, 33 (12):3585-3591. Funatsu T, Shimizu N, Kuruppu M, et al. 2015. Evaluation of Mode Ⅰ fracture toughness assisted by the numerical determination of k-resistance[J]. Rock Mechanics and Rock Engineering, 48 (1):143-157. doi: 10.1007/s00603-014-0550-8 Ghazvinian A, Sarfarazi V, Schubert W, et al. 2012. A study of the failure mechanism of planar non-persistent open joints using PFC2D[J]. Rock Mechanics and Rock Engineering, 45 (5):677-693. https://www.sciencedirect.com/science/article/pii/S0040195113002606 Hofmann H, Babadagli T, Yoon J S, et al. 2015. A grain based modeling study of mineralogical factors affecting strength, elastic behavior and micro fracture development during compression tests in granites[J]. Engineering Fracture Mechanics, 147:261-275. doi: 10.1016/j.engfracmech.2015.09.008 Huang D, Cen D F. 2013a. Mechanical responses and energy dissipation mechanism of rock specimen with a single fissure under static and dynamic uniaxial compression using particle flow code simulations[J]. Chinese Journal of Rock Mechanics and Engineering, 32 (9):1926-1936. https://www.researchgate.net/publication/286195466_Mechanical_responses_and_energy_dissipation_mechanism_of_rock_specimen_with_a_single_fissure_under_static_and_dynamic_uniaxial_compression_using_particle_flow_code_simulations Huang D, Cen D F, Huang R Q. 2013b. Influence of medium strain rate on sandstone with a single pre-crack under uniaxial compression using PFC simulation[J]. Rock and Soil Mechanics, 34 (2):535-545. https://www.researchgate.net/publication/286195469_Influence_of_medium_strain_rate_on_sandstone_with_a_single_pre-crack_under_uniaxial_compression_using_PFC_simulation Huang D, Jin H H, Huang R Q. 2011. Mechanism of fracture mechanics and physical model test of rocks crack expanding under tension-shear stress[J]. Rock and Soil Mechanics, 32 (4):997-1002. https://www.researchgate.net/publication/286991194_Mechanism_of_fracture_mechanics_and_physical_model_test_of_rocks_crack_expanding_under_tension-shear_stress Huang Y H, Yang S Q. 2014. Particle flow simulation of macro-and meso-mechanical behavior of red sandstone containing two pre-existing non-coplanar fissures[J]. Chinese Journal of Rock Mechanics and Engineering, 33 (8):1644-1653. http://industry.wanfangdata.com.cn/dl/Detail/Periodical?id=Periodical_yslxygcxb201408015 Itasca Consulting Group Inc. 2003. Users' manual for particle flow code in 2 dimensions(PFC2D), version 3. 0[R]. Minneapolis, Minnesota. Itasca Consulting Group Inc. 2008. Users' manual for particle flow code in 2 dimensions(PFC2D), version 4. 0[R]. Minneapolis, Minnesota. Itasca Consulting Group Inc. 2014. Users' manual for particle flow code(PFC), version 5. 0[R]. Minneapolis, Minnesota. Ivars D M, Pierce M E, Darcel D, et al. 2011. The synthetic rock mass approach for jointed rock mass modeling[J]. International Journal of Rock Mechanics and Mining Sciences, 48 (2):219-244. doi: 10.1016/j.ijrmms.2010.11.014 Jiang M J, Chen H, Zhang N, et al. 2014. Distinct element numerical analysis of crack evolution in rocks containing pre-existing double flaw[J]. Rock and Soil Mechanics, 35 (11):3259-3268, 3288. https://www.researchgate.net/publication/287291804_Distinct_element_numerical_analysis_of_crack_evolution_in_rocks_containing_pre-existing_double_flaw Jiang M J, Chen H. 2012. Numerical investigations on mechanisms of crack propagation and coalescence in rock by distinct element method[C]//National Conference on Computational Mechanics of Granular Materials(CMGM-2012). Zhangjiajie: [s. n. ]: 328-339. Jiang M J, Fang W, Si M J. 2015. Calibration of micro-parameters of parallel bonded model for rocks[J]. Journal of Shandong University(Engineering Science), 45 (4):50-56. Jiang M J, Yu H S, Harris D. 2006. Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 30 (8):723-761. doi: 10.1002/(ISSN)1096-9853 Jiang M J, Yu H S, Leroueil S. 2007. A simple and efficient approach to capturing bonding effect in naturally micro-structured sands by discrete element method[J]. International Journal for Numerical Methods in Engineering, 69 (6):1158-1193. doi: 10.1002/(ISSN)1097-0207 Lajtai E Z. 1974. Brittle fracture in compression[J]. International Journal of Fracture, 10 (4):525-536. doi: 10.1007/BF00155255 Lee H, Jeon S. 2011. An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression[J]. International Journal of Solids and Structures, 48 (6):979-999. doi: 10.1016/j.ijsolstr.2010.12.001 Li F, Li X F. 2013. Micro-numerical simulation on mechanism of fracture coalescence between two pre-existing flaws arranged in echelon[J]. Journal of Shenzhen University Science and Engineering, 30 (2):190-194. doi: 10.3724/SP.J.1249.2013.02190 Li X B. 2016. Failure analysis of cracked rock specimen under direct tension based on PFC simulation[J]. Water Resources and Power, 34 (3):124-127. Liu H W, Yang C. 2016. Micro-analysis of uniaxial compression of cracked rock containing open or closing fissure based on PFC[J]. Water Resources and Power, 34 (1):131-135. doi: 10.1007/s10409-015-0444-3.pdf Ming H J, Xu X F, Liang B. 2013. Simulation of rock failure mechanism of different fracture apertures using particle flow code[J]. Journal of China Three Gorges University(Natural Sciences), 35 (6):63-66. http://d.wanfangdata.com.cn/Periodical_whsldldxxb-yc201306014.aspx Ni H M, Huang Y H, Liu X R. 2014. Particle flow simulation on loading rate effects of red sandstone containing two pre-existing fissures[J]. Chinese Journal of Underground Space and Engineering, 10 (5):1010-1016. Niu L X, Xin Y Y. 2015. Analysis on relationship between macro-parameters and micro-parameters in PFC2D model based on orthogonal design:case of rock uniaxial compression numerical test[J]. Yangtze River, 46 (16):53-57, 71. https://www.researchgate.net/publication/254542070_Simulation_of_the_Mechanical_Behavior_of_Discontinuous_Rock_Masses_Using_a_Bonded-particle_Model Park C H, Bobet A. 2009. Crack coalescence in specimens with open and closed flaws:A comparison[J]. International Journal of Rock Mechanics & Mining Sciences, 46 (5):819-829. https://www.sciencedirect.com/science/article/pii/S1365160909000410 Potyondy D O, Cundall P A. 2004. A bonded-particle model for rock[J]. International Journal of Rock Mechanics and Mining Sciences, 41 (8):1329-1364. doi: 10.1016/j.ijrmms.2004.09.011 Potyondy D O. 2012. A flat-jointed bonded-particle material for hard rock[C]//Proceedings of the 46th US Rock Mechanics/Geomechanics Symposium. Chicago: [s. n. ]: 24-27. Shu Y, Wu J M, Yue L, et al. 2016. Numerical simulation of mechanical behavior of single fractured rock mass under direct shear[J]. Journal of PLA University of Science and Technology(Natural Science Edition), 17 (5):424-432. Su H J, Jing H W, Zhao H H, et al. 2014. Experimental study on the influence of longitudinal fissure on mechanics characteristic of sandstone[J]. Journal of Mining & Safety Engineering, 31 (4):644-649. Tang H M, Zhang J H, Chen H K. 2016. Laboratory tests on failure mechanism of fractured rock under compression[J]. Journal of Engineering Geology, 24 (3):363-368. Tang Q, Li Y A. 2015. Particle flow simulation on the influence of confinement on crack propagation in pre-cracked rock[J]. Journal of Yangtze River Scientific Research Institute, 32 (4):81-85. Wang W H, Wang X J, Jiang H T, et al. 2014. Experimental research on mechanical properties of rocklike specimens containing single cracks of different inclination angles under uniaxial compression[J]. Science & Technology Review, 32(28/29):48-53. Wang Y F, Zheng X J, Zhao H B, et al. 2015. Characteristics of coal's strength deformation and acoustic emission under biaxial loading with particle flow code[J]. Journal of Engineering Geology, 23 (6):1059-1065. Whittaker B N, Singh R N, Sun G. 1992. Rock fracture mechanics:Principles, design and applications[M]. Amsterdam:Elsevier. Wong L N Y, Einstein H H. 2009. Crack coalescence in molded gypsum and Carrara marble:part 1. macroscopic observations and interpretation[J]. Rock Mechanics and Rock Engineering, 42 (3):513-545. doi: 10.1007/s00603-008-0003-3 Wong R H C, Tang C A, Chau K T, et al. 2002. Splitting failure in brittle rocks containing pre-existing flaws under uniaxial compression[J]. Engineering Fracture Mechanics, 69 (17):1853-1871. doi: 10.1016/S0013-7944(02)00065-6 Xia M, Zhao C B. 2014. Dimensional analysis of effects of microscopic parameters on macroscopic parameters for clump parallel-bond model[J]. Chinese Journal of Rock Mechanics and Engineering, 33 (2):327-338. https://www.researchgate.net/publication/285932504_Dimensional_analysis_of_effects_of_microscopic_parameters_on_macroscopic_parameters_for_clump_parallel-bond_model Xu J M, Xie Z L, Jia H T. 2010. Simulation of mesomechanical properties of limestone using particle flow code[J]. Rock and Soil Mechanics, 31(S2):390-395. https://www.researchgate.net/publication/289350783_Simulation_of_mesomechanical_properties_of_limestone_using_particle_flow_code Yang S Q, Huang Y H, Liu X R. 2014. Particle flow analysis on tensile strength and crack coalescence behavior of brittle rock containing two pre-existing fissures[J]. Journal of China University of Mining & Technology, 43 (2):220-226. Yang S Q, Huang Y H. 2014. Experiment and particle flow simulation on crack coalescence behavior of sandstone specimens containing double holes and a single fissure[J]. Journal of Basic Science and Engineering, 22 (3):584-597. https://www.researchgate.net/publication/287575523_Experiment_and_particle_flow_simulation_on_crack_coalescence_behavior_of_sandstone_specimens_containing_double_holes_and_a_single_fissure Yoon J S, Zang A, Stephansson O. 2012. Simulating fracture and friction of Aue granite under confined asymmetric compressive test using clumped particle model[J]. International Journal of Rock Mechanics & Mining Sciences, 49 (1):68-83. https://www.sciencedirect.com/science/article/pii/S1365160911001894 Yoon J S. 2007. Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation[J]. International Journal of Rock Mechanics & Mining Sciences, 44 (6):871-889. https://www.sciencedirect.com/science/article/pii/S1365160907000135 Zeng Q D, Yao J, Huo J D. 2015. Inversion of rock meso-mechanical parameters based on parallel particle swarm optimization(PSO)algorithm[J]. Journal of Xi'an Shiyou University(Natural Science Edition), 30 (4):27-32. https://www.researchgate.net/publication/282926231_Inversion_of_rock_meso-mechanical_parameters_based_on_parallel_particle_swarm_optimization_PSO_algorithm Zhang X P, Wong L N Y. 2013. Crack initiation, propagation and coalescence in rock-like material containing two flaws:a numerical study based on bonded-particle model approach[J]. Rock Mechanics and Rock Engineering, 46 (5):1001-1021. doi: 10.1007/s00603-012-0323-1 Zhang Z X, Kou S Q, Lindqvist P A, et al. 1998. The relationship between the fracture toughness and tensile strength of rock[M]. Strength theories: applications, development & prospects for 21st century. Beijing/NewYork: Science Press: 215-223. Zhao C B, Hobbs B E, Ord A, et al. 2007. Particle simulation of spontaneous crack generation problems in large-scale quasi-static systems[J]. International Journal for Numerical Methods in Engineering, 69 (11):2302-2329. doi: 10.1002/(ISSN)1097-0207 Zhong B B, Zhang Y B, Li H. 2014. Study of mechanisms of crack propagation of rock based on RFPA2D[J]. Journal of Wuhan University of Technology, 36 (2):82-88. Zhou J, Wang J Q, Zeng Y, et al. 2009. Slope safety factor by methods of particle flow code strength reduction and gravity increase[J]. Rock and Soil Mechanics, 30 (6):1549-1554. https://www.researchgate.net/publication/289736639_Slope_safety_factor_by_methods_of_particle_flow_code_strength_reduction_and_gravity_increase Zhou Y, Gao Y T, Wu S C, et al. 2015. An equivalent crystal model for mesoscopic behaviour of rock[J]. Chinese Journal of Rock Mechanics and Engineering, 34 (3):511-519. https://www.researchgate.net/publication/281999448_An_equivalent_crystal_model_for_mesoscopic_behaviour_of_rock Zhou Y, Wu S C, Jiao J J, et al. 2011. Research on mesomechanical parameters of rock and soil mass based on BP neural network[J]. Rock and Soil Mechanics, 32 (12):3821-3826. https://www.researchgate.net/publication/287529732_Research_on_mesomechanical_parameters_of_rock_and_soil_mass_based_on_BP_neural_network 岑夺丰, 黄达. 2014a.高应变率单轴压缩下岩体裂隙扩展的细观位移模式[J].煤炭学报, 39 (3):436-444. http://www.cnki.com.cn/Article/CJFDTOTAL-MTXB201403008.htm 岑夺丰, 黄达, 黄润秋. 2014b.岩质边坡断续裂隙阶梯状滑移模式及稳定性计算[J].岩土工程学报, 36 (4):695-706. http://manu31.magtech.com.cn/Jwk_ytgcxb/CN/abstract/abstract15696.shtml 岑夺丰. 2013. 岩质边坡阶梯状滑移机制颗粒流模拟及稳定性研究[D]. 重庆: 重庆大学. 陈枫. 2002. 岩石压剪断裂的理论与实验研究[D]. 长沙: 中南大学. 陈鹏宇, 余宏明. 2016.平直节理黏结颗粒材料宏细观参数关系及细观参数的标定[J].土木建筑与环境工程, 38 (5):74-83. http://www.cnki.com.cn/Article/CJFDTOTAL-MTXB2017S1011.htm 陈鹏宇. 2015. 岩质高边坡坡体结构特征分析与稳定性研究——以焦作市龙寺矿山岩质高边坡为例[D]. 武汉: 中国地质大学(武汉). 陈秀云. 2015.单一闭合中心裂隙对岩石单轴压缩破坏特征的影响[J].长江科学院院报, 32 (9):104-110. 邓华锋, 朱敏, 李建林, 等. 2012.砂岩Ⅰ型断裂韧度及其与强度参数的相关性研究[J].岩土力学, 33 (12):3585-3591. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ytlx201212009 黄达, 岑夺丰. 2013a.单轴静-动相继压缩下单裂隙岩样力学响应及能量耗散机制颗粒流模拟[J].岩石力学与工程学报, 32 (9):1926-1936. doi: 10.3969/j.issn.1000-6915.2013.09.026 黄达, 岑夺丰, 黄润秋. 2013b.单裂隙砂岩单轴压缩的中等应变率效应颗粒流模拟[J].岩土力学, 34 (2):535-545. http://www.cnki.com.cn/Article/CJFDTotal-YTLX201302035.htm 黄达, 金华辉, 黄润秋. 2011.拉剪应力状态下岩体裂隙扩展的断裂力学机制及物理模型试验[J].岩土力学, 32 (4):997-1002. http://www.cqvip.com/QK/94551X/201104/37228120.html 黄彦华, 杨圣奇. 2014.非共面双裂隙红砂岩宏细观力学行为颗粒流模拟[J].岩石力学与工程学报, 33 (8):1644-1653. http://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201408017.htm 蒋明镜, 陈贺, 张宁, 等. 2014.含双裂隙岩石裂纹演化机理的离散元数值分析[J].岩土力学, 35 (11):3259-3268, 3288. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ytlx201411030 蒋明镜, 陈贺. 2012. 岩石裂纹扩展与贯通机制的离散元数值分析[C]//2012颗粒材料计算力学会议. 张家界: [出版者不详]: 328-339. 蒋明镜, 方威, 司马军. 2015.模拟岩石的平行黏结模型微观参数标定[J].山东大学学报(工学版), 45 (4):50-56. doi: 10.6040/j.issn.1672-3961.0.2014.183 李凡, 李雪峰. 2013.两条雁行预制裂隙贯通机制的细观数值模拟[J].深圳大学学报(理工版), 30 (2):190-194. http://d.wanfangdata.com.cn/Periodical_szdxxb201302014.aspx 李现宾. 2016.裂隙岩石直接拉伸断裂破坏的颗粒流模拟分析[J].水电能源科学, 34 (3):124-127. 刘华伟, 杨晨. 2016.闭合与非闭合裂隙岩石单轴压缩的颗粒流细观分析[J].水电能源科学, 34 (1):131-135. http://www.cqvip.com/QK/95255X/201601/667698179.html 明华军, 徐小峰, 梁波. 2013.不同裂隙张开度下岩石材料破坏的颗粒离散元模拟[J].三峡大学学报(自然科学版), 35 (6):63-66. http://d.wanfangdata.com.cn/Periodical_whsldldxxb-yc201306014.aspx 倪红梅, 黄彦华, 刘相如. 2014.断续双裂隙红砂岩加载速率效应颗粒流分析[J].地下空间与工程学报, 10 (5):1010-1016. 牛林新, 辛酉阳. 2015.基于正交设计的颗粒流模型宏细观参数相关分析——以岩石单轴压缩数值试验为例[J].人民长江, 46 (16):53-57, 71. http://www.cnki.com.cn/Article/CJFDTOTAL-RIVE201516013.htm 舒杨, 吴继敏, 岳翎, 等. 2016.直剪条件下单裂隙岩体力学行为数值模拟试验[J].解放军理工大学学报(自然科学版), 17 (5):424-432. 苏海健, 靖洪文, 赵洪辉, 等. 2014.纵向裂隙对砂岩力学特性影响试验研究[J].采矿与安全工程学报, 31 (4):644-649. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=ksylydbgl201404025 唐红梅, 张金浩, 陈洪凯. 2016.含裂隙岩石的受压破坏机理研究[J].工程地质学报, 24 (3):363-368. http://www.gcdz.org/CN/abstract/abstract11981.shtml 唐谦, 李云安. 2015.围压对岩石裂纹扩展影响的颗粒流模拟研究[J].长江科学院院报, 32 (4):81-85. http://d.wanfangdata.com.cn/Periodical_cjkxyyb201504016.aspx 王卫华, 王小金, 姜海涛, 等. 2014.单轴压缩作用下含不同倾角裂隙的类岩石试样力学特性[J].科技导报, 32(28/29):48-53. http://www.cnki.com.cn/Article/CJFDTOTAL-KJDB2014Z2020.htm 王云飞, 郑晓娟, 赵洪波, 等. 2015.双向加载煤岩变形与声发射特性颗粒流研究[J].工程地质学报, 23 (6):1059-1065. http://www.gcdz.org/CN/abstract/abstract11910.shtml 夏明, 赵崇斌. 2014.簇平行黏结模型中微观参数对宏观参数影响的量纲研究[J].岩石力学与工程学报, 33 (2):327-338. http://industry.wanfangdata.com.cn/dl/Detail/Periodical?id=Periodical_yslxygcxb201402014 徐金明, 谢芝蕾, 贾海涛. 2010.石灰岩细观力学特性的颗粒流模拟[J].岩土力学, 31 (增2):390-395. https://www.wenkuxiazai.com/doc/3f04297b27284b73f2425036-3.html 杨圣奇, 黄彦华, 刘相如. 2014a.断续双裂隙岩石抗拉强度与裂纹扩展颗粒流分析[J].中国矿业大学学报, 43 (2):220-226. http://www.cnki.com.cn/Article/CJFDTOTAL-ZGKD201402007.htm 杨圣奇, 黄彦华. 2014b.双孔洞裂隙砂岩裂纹扩展特征试验与颗粒流模拟[J].应用基础与工程科学学报, 22 (3):584-597. 曾青冬, 姚军, 霍吉东. 2015.基于并行PSO算法的岩石细观力学参数反演研究[J].西安石油大学学报(自然科学版), 30 (4):27-32. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=xasyxyxb201504006 钟波波, 张永彬, 李宏. 2014.基于RFPA2D的岩石裂纹扩展模式的研究[J].武汉理工大学学报, 36 (2):82-88. http://www.docin.com/p-526796309.html 周健, 王家全, 曾远, 等. 2009.颗粒流强度折减法和重力增加法的边坡安全系数研究[J].岩土力学, 30 (6):1549-1554. http://www.cqvip.com/QK/94551X/200906/30528366.html 周喻, 高永涛, 吴顺川, 等. 2015.等效晶质模型及岩石力学特征细观研究[J].岩石力学与工程学报, 34 (3):511-519. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yslxygcxb201503008 周喻, 吴顺川, 焦建津, 等. 2011.基于BP神经网络的岩土体细观力学参数研究[J].岩土力学, 32 (12):3821-3826. doi: 10.3969/j.issn.1000-7598.2011.12.045 -
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