Numerical modeling of the energy dissipation and fragmentation of copper-bearing rock under impact load
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摘要: 为了研究冲击荷载作用下含铜矿岩的破碎块度与能量耗散关系，借助分离式霍普金森压杆试验装置，分析不同冲击荷载下含铜凝灰岩的力学特性及能量传递规律，结合分形理论构建耗散能与矿岩破碎块度之间的关系；同时，基于有限离散元方法（finite discrete element method，FDEM）模拟矿岩的裂纹扩展行为。结果表明：随着入射能的增加，透射能、耗散能、反射能三者的能量分布规律基本保持一致，即透射能、耗散能、反射能依次减小；根据耗散能的不同，碎石块度分布也呈现出明显的差异性。当耗散能由19.52 J增加至105.72 J时，矿岩的平均块度从27.98 mm降低至16.94 mm，分形维数提升了26.43%，表明耗散能越高，矿岩的宏观破碎程度越剧烈，破碎块度的数目越多，碎块粒径越小，均匀性越好；随着冲击荷载的增大，裂纹起裂时间缩短，拉伸裂纹数量占总裂纹数量的比重提高。FDEM数值计算方法的应用可为深入解析岩石断裂破坏特性提供新的思路。Abstract: To understand the relationship between fragmentation and energy dissipation in copper-bearing ore rock subjected to impact loading, a split Hopkinson pressure bar (SHPB) testing apparatus was employed to study the mechanical properties and energy transfer mechanisms of copper-bearing tuff under varying impact loads. Additionally, fractal theory was used to establish the correlation between dissipated energy and rock fragmentation. Utilizing the finite discrete element method (FDEM), numerical simulations of crack propagation within the rock were conducted. The results indicate that as the incident energy increases, the distribution patterns of the transmission energy, dissipated energy and reflection energy remain consistent, which are characterized by transmission energy, dissipated energy and reflection energy decreased successively. Furthermore, significant variations in fragment size distribution are observed with changes in dissipated energy. Specifically, as dissipated energy increases from 19.52 J to 105.72 J, the average fragment size decreases from 27.98 mm to 16.94 mm, while the fractal dimension increases by 26.43%. This suggests that higher dissipated energy results in more extensive macroscopic fragmentation, an increase in the number of fragments, smaller particle sizes and enhanced uniformity. As the impact load intensifies, the time to crack initiation decreases, and the proportion of tensile cracks relative to total cracks increases. The application of the FDEM offers new insights into the fracture and failure characteristics of rocks.
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金属铍具有中子散射截面大、吸收截面小、硬度高、模量高、比强高、热学性能良好等特性，因此被广泛应用于航空航天、军事工业、医疗设备、焊接技术等多个技术领域，如中子反射层，反应堆第一壁材料、中子慢化剂，航空航天结构部件、精密仪表、光学器件及X射线管窗口等。国外已开展大量金属铍的变形行为研究，而国内开展的相关研究较少，且主要集中在常温静态拉伸性能方面，对其压缩力学行为尤其是动态压缩特性方面报道较少[1-9]。王零森等[1]研究了晶粒尺寸对铍静态拉伸力学性能的影响，发现随着晶粒度逐渐细化，铍材料的强度显著提高，而晶粒过粗或过细，延伸率均下降。许德美等[2-3]研究了组织缺陷对金属铍室温拉伸断裂行为的影响，其分析结果表明铍的“脆性”特征主要来源于杂质、片状晶体疏松和孔洞等初始缺陷，最关键因素是杂质的尺寸、间距和其在材料内部的分布形态。W.R.Blumenthal等[4-5]对不同制备工艺下的铍进行了较为系统的研究。实验结果表明，铍的压缩应力应变响应具有较强的应变率敏感性和一定的热软化效应，并指出孪生是高应变率下铍变形的主要机制。D.W.Brown等[6-8]系统开展了应变率对热压和轧制铍的力学性能和变形机理的研究工作，分析结果表明屈服强度对应变率不敏感，而加工硬化则受织构的影响具有较强的率相关性。T.Nicholas[9]和D.Breithaupt[10]研究了铍在常温102~103 s-1应变率下的动态压缩性能，结果表明铍具有良好的塑性，应变增大至0.25时样品才发生断裂。由此可见，国外开展的相关研究工作重点关注制备工艺、温度、应变率等条件对金属铍滑移及孪晶变形机制的影响研究，获得描述金属铍变形织构行为的本构模型参数。国内开展的研究则主要围绕金属铍静态拉伸应力状态下的“脆性”行为的微观变形机制，对其压缩行为研究工作较少，尤其是动态加载下温度、应变速率对其变形行为的影响未见相关研究报道。
本文中利用材料实验机及Hopkinson杆装置系统开展了热等静压金属铍在不同温度、应变率下的压缩力学行为研究，获得金属铍压缩载荷下强度、塑性与实验温度、应变率之间的对应关系。并采用Johnson-Cook本构模型对获得的应力应变曲线进行拟合，模型计算结果与实验结果吻合较好。
1. 实验材料及方法
铍在机加后表面会有较大的残余应力，为了消除残余应力对测量结果的影响[11]，室温力学实验前对样品进行了蚀刻处理，蚀刻剂配方为：H3PO4，750 mL；H2SO4，30 mL；Cr2O3，71 mg；H2O，200 mL。蚀刻方法为将铍试样放入酸洗液约50 s取出，用蒸馏水等清洗干净。
静态力学实验在CMT5105型材料试验机及其配置的高温真空炉中进行，高温炉温度控制精度为±3 ℃，真空度优于1×10-2 Pa，试样在1 h内加热到规定温度，保温15 min后开始实验，应变率为1.0×10-3 s-1，测试温度范围为室温至800 ℃。动态压缩实验采用∅10 mm的Hopkinson杆装置。试样为∅5 mm×5 mm的圆柱体，应变率范围为0.5×103~2.5×103 s-1, 在常温下进行。
2. 实验结果与分析
图 1所示为铍在不同温度下的准静态压缩实验结果。由图 1应力应变曲线可以看出，金属铍在室温至800 ℃的温度范围内压缩变形具有良好的塑性。屈服强度和流动应力随实验温度升高而降低，加工硬化行为也随之降低。图 2所示为不同固定应变下的流动应力随实验温度的变化。由图中可以看到，在室温至200 ℃时，不同固定应变下流动应力均下降较快，高于200 ℃时流动应力下降趋势变缓，呈线性下降特征。当实验温度高于400 ℃时，不同应变下的流动应力值基本一致，这表明此时材料的塑性变形行为趋于理性塑性流动。
图 1 金属铍在准静态条件下应力应变关系Figure 1. Relation between stress and strain under quasi-static condition
图 2 金属铍在准静态条件下流动应力随温度变化曲线Figure 2. Relation between flow stress and temprature under quasi-static condition图 3所示为铍的动态压缩实验结果。可以看出，铍的屈服强度和加工硬化行为随应变率增大而显著增大，在初始变形阶段，加工硬化行为呈现非线性特征，随变形量增大，转变为线性硬化。由文献[4]可知，准静态和动态加载下，金属铍的塑性变形控制机制有显著区别。与大多数对称性低、滑移系统少的密排六方晶系金属一样，由于晶体的取向不利于发生滑移，孪生成为铍塑性变形的重要方式。在初始变形阶段，变形机制由位错滑移控制，随着变形增大，位错滑移困难，通过孪生协调变形，尤其在动态加载过程中，晶粒内部将产生大量的孪晶，由于滑移与孪生机制的竞争导致了不同应变率、不同应变下金属铍屈服强度和加工硬化行为的显著区别。
3. 本构模型
Johnson-Cook模型是目前应用最广泛的本构模型之一，模型中将流动应力表述为应变硬化效应、应变率效应和温度软化效应的乘积，方程的基本形式如下：
σ=(A+Bεnp)(1+Cln˙ε˙ε0)(1−T∗m) (1) 式中:σ为Von-Mises流动应力，εp为等效塑性应变，A为准静态下的屈服应力，B为应变硬化系数，n为应变硬化指数，˙ε0为参考应变率(可取准静态应变率)，C为应变率敏感系数，T*为温度相关项，具体表达式为(T-Tr)/(Tm-Tr), Tr和Tm分别为参考温度和熔化温度，一般取Tr为300 K，m为热软化系数。由式(1)可见，Johnson-Cook本构模型忽略了材料变形历史的影响，即如果材料服从Johnson-Cook本构模型，则不同应变率下的应力应变曲线是相似的。
而由图 1~3中的应力应变曲线可以看到，不同温度或应变率下铍的应力应变曲线呈发散趋势，传统的Johnson-Cook本构模型已不适用。因此，本文中采用一个修正的Johnson-Cook本构模型对实验数据进行拟合，在应变硬化项中增加屈服强度温度相关线性函数，同时参考Zerrilli-Armstrong本构模型中描述hcp晶体结构材料变形硬化的函数关系式, 在幂指数应变硬化项中添加应变率指数硬化项和温度指数软化项，分别描述温度、变形历史对材料屈服强度和流动应力的影响，以及流动应力随应变率明显的增加趋势, 其表达式为：
σ=[A(1−A1T∗)+Bεnpea˙ε(B1+B2eβT∗)](1+Cln˙ε˙ε0) (2) 和传统Johnson-Cook模型相比，修正模型中增加了4个参数。取准静态应变率10-3 s-1为参考应变率，Tm=1 557 K。本构拟合参数为：A=424 MPa, B=1 010 MPa, A1=1.487, B1=0.107 3, B2=0.885 4, n=0.485, α=0.000 39, β=-13.83, C=0.015。
采用修正模型计算结果与实验结果对比如图 4所示，实线为采用修正Johnson-Cook本构模型的计算结果。可以看到，模型的计算结果与实验结果符合较好，修正后的Johnson-Cook本构模型能够较好地描述金属铍在不同温度、应变和应变率下的压缩变形行为。
图 4 修正Johnson-Cook模型计算结果与实验结果对比Figure 4. Comparison of experimental results with calculated results by modified Johnson-Cook model4. 结论
本文中研究了较宽温度范围和应变率下热等静压金属铍的压缩力学行为。结果表明铍的屈服强度和加工硬化行为随应变率的提高而显著增大，随温度的升高而降低。常温下其加工硬化行为在初始变形阶段呈现非线性特征，随变形增大转变为线性硬化。温度高于400 ℃时，其变形行为趋于理性塑性流动。考虑温度、变形历史对材料屈服强度和加工硬化的影响，对Johnson-Cook模型进行了修正，修正后的本构模型预测结果和实验结果吻合较好。
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图 4 冲击气压与入射能曲线关系
Figure 4. Relationship between impact pressure and incident energy curve
图 6 冲击荷载下含铜矿岩能量比率传递规律
Figure 6. Energy ratio transfer of copper bearing rock under impact load
图 7 不同耗散能下含铜矿岩的破碎模式
Figure 7. Fracture patterns of copper bearing rocks under different dissipated energies
图 8 不同耗散能与含铜矿岩破碎块度分布
Figure 8. Mass distribution against fragment size for different dissipated energy by copper bearing rocks
图 9 不同耗散能与矿岩破碎块度的分布
Figure 9. Distribution of copper-bearing rock fragmentation for different dissipated energies
图 10 不同耗散能条件下典型lg[M(r)/MT]-lgr关系曲线
Figure 10. Typical lg[M(r)/MT]-lgr curves under different dissipated energies
图 11 耗散能与分形维数关系曲线
Figure 11. Relationship between fractal dimension and dissipated energy
图 14 不同冲击气压下含铜凝灰矿岩的裂纹演变图（蓝色代表拉伸裂纹，红色代表剪切裂纹）
Figure 14. Crack evolution diagram of copper-bearing Tuff specimens under different impact air pressures (blue represents tensile cracks, and red represents shear cracks)
表 1 含铜矿岩基本物理力学参数
Table 1. Basic physical and mechanical parameters of copper-bearing rock specimen
编号 密度/
(g·cm−3)纵波波速/
(m·s−1)弹性模量/
GPa泊松比 抗压强度/
MPaJ-1 3.10 3 549 93.35 0.33 59.23 
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表 2 含铜矿岩的冲击实验数据
Table 2. SHPB test data of copper-bearing rock samples
编号 冲击气压/
MPa平均应
变率/s−1峰值应力/
MPaWi/J Wr/J Wt/J Wd/J A-3 0.5 30.68 108.03 63.34 7.24 45.13 10.62 B-2 0.6 35.71 119.72 81.67 5.73 55.75 19.51 C-4 0.7 44.25 141.35 105.92 7.32 66.10 31.57 D-1 0.8 50.93 163.19 130.76 8.05 74.19 47.75 E-3 0.9 53.62 189.55 168.28 23.94 83.45 60.60 F-2 1.0 59.15 200.93 203.33 37.88 89.99 75.12 G-4 1.1 64.81 249.80 222.91 43.46 93.01 85.52 H-1 1.2 77.39 265.90 267.09 62.21 99.06 105.72
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表 3 含铜矿岩破碎块度筛分试验结果
Table 3. Test screening results of crushed copper-bearing rock fragments
编号 Wd/J 各等级粒径岩矿碎块的质量/g 平均块度/
mm<0.3 mm <0.5 mm <1.0 mm <2.0 mm <4.0 mm <9.5 mm <16.0 mm <19.0 mm <26.5 mm <37.5 mm B2-0.6 19.52 0.04 0.18 0.13 0.31 0.16 1.35 2.95 12.8 36.44 123.42 27.98 C4-0.7 31.58 0.09 0.13 0.25 0.55 0.64 3.03 4.50 18.16 91.39 51.51 23.29 D1-0.8 47.75 0.11 1.52 2.46 3.74 3.39 12.10 18.87 24.19 47.12 53.92 20.54 E3-0.9 60.61 0.07 0.12 0.32 0.79 0.78 9.06 25.52 33.49 55.18 20.42 19.62 F2-1 75.13 0.10 0.24 0.54 1.33 1.25 9.85 40.75 39.61 22.46 20.47 18.28 G4-1.1 85.53 0.15 0.37 0.75 1.55 1.38 16.84 44.16 30.27 69.63 0 16.92 H3-1.2 105.72 0.27 0.68 1.20 2.60 1.92 20.17 51.22 32.99 46.95 12.74 16.94
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[1] 李鹏远, 周平, 唐金荣, 等. 中国铜矿资源供应风险识别与评价: 基于长周期历史数据分析预测法 [J]. 中国矿业, 2019, 28(7): 44–51. DOI: 10.12075/j.issn.1004-4051.2019.07.027.LI P Y, ZHOU P, TANG J R, et al. Identification and evaluation of copper supply risk for China: using method of long-term historical data analysis [J]. China Mining Magazine, 2019, 28(7): 44–51. DOI: 10.12075/j.issn.1004-4051.2019.07.027. [2] 黎立云, 谢和平, 鞠杨, 等. 岩石可释放应变能及耗散能的实验研究 [J]. 工程力学, 2011, 28(3): 35–40. DOI: 10.6052/j.issn.1000-4750.2009.08.0584.LI L Y, XIE H P, JU Y, et al. Experimental investigations of releasable energy and dissipative energy within rock [J]. Engineering Mechanics, 2011, 28(3): 35–40. DOI: 10.6052/j.issn.1000-4750.2009.08.0584. [3] 武仁杰, 李海波. SHPB冲击作用下层状千枚岩多尺度破坏机理研究 [J]. 爆炸与冲击, 2019, 39(8): 083106. DOI: 10.11883/bzycj-2019-0187.WU R J, LI H B. Multi-scale failure mechanism analysis of layered phyllite subject to impact loading [J]. Explosion and Shock Waves, 2019, 39(8): 083106. DOI: 10.11883/bzycj-2019-0187. [4] CHO S H, OGATA Y, KANEKO K. Strain-rate dependency of the dynamic tensile strength of rock [J]. International Journal of Rock Mechanics and Mining Sciences, 2003, 40(5): 763–777. DOI: 10.1016/S1365-1609(03)00072-8. [5] 江益辉. 冲击荷载作用下岩石峰后损伤破坏特性研究 [D]. 长沙: 中南大学, 2014: 48–53.JIANG Y H. Study on post failure behaviors of rock under impact loading [D]. Changsha: Central South University, 2014: 48–53. [6] 尤业超, 李二兵, 谭跃虎, 等. 基于能量耗散原理的盐岩动力特性及破坏特征分析 [J]. 岩石力学与工程学报, 2017, 36(4): 843–851. DOI: 10.13722/j.cnki.jrme.2016.0503.YOU Y C, LI E B, TAN Y H, et al. Analysis on dynamic properties and failure characteristics of salt rock based on energy dissipation principle [J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(4): 843–851. DOI: 10.13722/j.cnki.jrme.2016.0503. [7] PING Q, WU M J, YUAN P, et al. Dynamic splitting experimental study on sandstone at actual high temperatures under different loading rates [J]. Shock and Vibration, 2020, 2020: 8867102. DOI: 10.1155/2020/8867102. [8] LI E B, GAO L, JIANG X Q, et al. Analysis of dynamic compression property and energy dissipation of salt rock under three-dimensional pressure [J]. Environmental Earth Sciences, 2019, 78(14): 388. DOI: 10.1007/s12665-019-8389-7. [9] YU L Y, FU A Q, YIN Q, et al. Dynamic fracturing properties of marble after being subjected to multiple impact loadings [J]. Engineering Fracture Mechanics, 2020, 230: 106988. DOI: 10.1016/j.engfracmech.2020.106988. [10] WU Z J, CUI W J, FAN L F, et al. Mesomechanism of the dynamic tensile fracture and fragmentation behaviour of concrete with heterogeneous mesostructure [J]. Construction and Building Materials, 2019, 217: 573–591. DOI: 10.1016/j.conbuildmat.2019.05.094. [11] FUKUDA D, MOHAMMADNEJAD M, LIU H Y, et al. Development of a 3D hybrid finite-discrete element simulator based on GPGPU-parallelized computation for modelling rock fracturing under quasi-static and dynamic loading conditions [J]. Rock Mechanics and Rock Engineering, 2020, 53(3): 1079–1112. DOI: 10.1007/s00603-019-01960-z. [12] WU D, LI H B, FUKUDA D, et al. Development of a finite-discrete element method with finite-strain elasto-plasticity and cohesive zone models for simulating the dynamic fracture of rocks [J]. Computers and Geotechnics, 2023, 156: 105271. DOI: 10.1016/j.compgeo.2023.105271. [13] 柴少波, 王昊, 井彦林, 等. 充填节理岩石累积损伤动力压缩特性试验研究 [J]. 岩石力学与工程学报, 2020, 39(10): 2025–2037. DOI: 10.13722/j.cnki.jrme.2020.0310.CHAI S B, WANG H, JING Y L, et al. Experimental study on dynamic compression characteristics of rock with filled joints after cumulative damage [J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39(10): 2025–2037. DOI: 10.13722/j.cnki.jrme.2020.0310. [14] 滕骁, 卢玉斌, 陈兴, 等. 再生混凝土动态直接拉伸的试验研究 [J]. 振动与冲击, 2016, 35(9): 43–51. DOI: 10.13465/j.cnki.jvs.2016.09.008.TENG X, LU Y B, CHEN X, et al. Tests for dynamic direct tensile of recycled aggregate concrete [J]. Journal of Vibration and Shock, 2016, 35(9): 43–51. DOI: 10.13465/j.cnki.jvs.2016.09.008. [15] 魏威. 冲击载荷作用下活性材料的响应特性研究 [D]. 北京: 北京理工大学, 2016: 35–39.WEI W. Study on the dynamic responses of the active materialsunder impact loadings [D]. Beijing: Beijing Institute of Technology, 2016: 35–39. [16] 王建国, 雷振, 杨阳, 等. 饱水冻结花岗岩动态力学性状的应变率效应 [J]. 地下空间与工程学报, 2018, 14(5): 1292–1297.WANG J G, LEI Z, YANG Y, et al. Strain rate effect of dynamic mechanical characteristics of saturated freezing granite [J]. Chinese Journal of Underground Space and Engineering, 2018, 14(5): 1292–1297. [17] 袁芝斌. 大红山铜矿深部巷道围岩动态破碎耗能规律研究 [D]. 昆明: 昆明理工大学, 2021: 53–56. DOI: 10.27200/d.cnki.gkmlu.2021.000385.YUAN Z B. Research on the energy dissipation mechanism of dynamic fragmentation in surrounding rock of deep shafts in the Dahongshan copper mine [D]. Kunming: Kunming University of Science and Technology, 2021: 53–56. DOI: 10.27200/d.cnki.gkmlu.2021.000385. [18] 王浩. 大红山铜矿深埋变质灰岩动态响应特征研究 [D]. 昆明: 昆明理工大学, 2021: 68–69. DOI: 10.27200/d.cnki.gkmlu.2021.001943.WANG H. Study on the dynamic response characteristics of deeply buried metamorphic limestone in the Dahongshan copper mine [D]. Kunming: Kunming University of Science and Technology, 2021: 68–69. DOI: 10.27200/d.cnki.gkmlu.2021.001943. [19] 谢和平, 高峰. 岩石类材料损伤演化的分形特征 [J]. 岩石力学与工程学报, 1991, 10(1): 74–82.XIE H P, GAO F. The fractal features of the damage evolution of rock materials [J]. Chinese Journal of Rock Mechanics and Engineering, 1991, 10(1): 74–82. [20] 梁正召, 唐春安, 唐世斌, 等. 岩石损伤破坏过程中分形与逾渗演化特征 [J]. 岩土工程学报, 2007, 29(9): 1386–1391. DOI: 10.3321/j.issn:1000-4548.2007.09.017.LIANG Z Z, TANG C A, TANG S B, et al. Characteristics of fractal and percolation of rocks subjected to uniaxial compression during their failure process [J]. Chinese Journal of Geotechnical Engineering, 2007, 29(9): 1386–1391. DOI: 10.3321/j.issn:1000-4548.2007.09.017. [21] 李祥龙, 何丽华, 栾龙发, 等. 露天煤矿高台阶抛掷爆破爆堆形态模拟 [J]. 煤炭学报, 2011, 36(9): 1457–1462. DOI: 10.13225/j.cnki.jccs.2011.09.014.LI X L, HE L H, LUAN L F, et al. Simulation model for muckpile shape of high bench cast blasting in surface coal mine [J]. Journal of China Coal Society, 2011, 36(9): 1457–1462. DOI: 10.13225/j.cnki.jccs.2011.09.014. [22] 杨军, 王国生. 分形几何在岩石爆破研究中的应用 [J]. 爆破, 1995(4): 1–5. [23] 丁希平, 冯叔瑜, 魏伴云. 硐室爆破法采石级配预测 [J]. 爆炸与冲击, 1997, 17(4): 326–332. DOI: 10.11883/1001-1455(1997)04-0326-7.DING X P, FENG S Y, WEI B Y. Prediction of rock fragment distribution for chamber blasting [J]. Explosion and Shock Waves, 1997, 17(4): 326–332. DOI: 10.11883/1001-1455(1997)04-0326-7. [24] 杨仁树, 李炜煜, 杨国梁, 等. 炸药类型对富铁矿爆破效果影响的试验研究 [J]. 爆炸与冲击, 2020, 40(6): 065201. DOI: 10.11883/bzycj-2019-0396.YANG R S, LI W Y, YANG G L, et al. Experimental study on the blasting effects of rich-iron ore with different explosives [J]. Explosion and Shock Waves, 2020, 40(6): 065201. DOI: 10.11883/bzycj-2019-0396. [25] MUNJIZA A, OWEN D R J, BICANIC N. A combined finite-discrete element method in transient dynamics of fracturing solids [J]. Engineering Computations, 1995, 12(2): 145–174. DOI: 10.1108/02644409510799532. [26] MUNJIZA A. Special issue on the discrete element method: aspects of recent developments in computational mechanics of discontinua [J]. Engineering Computations, 2009, 26(6). DOI: 10.1108/ec.2009.18226faa.001. [27] YAN C Z, ZHENG Y C, WANG G. A 2D adaptive finite-discrete element method for simulating fracture and fragmentation in geomaterials [J]. International Journal of Rock Mechanics and Mining Sciences, 2023, 169: 105439. DOI: 10.1016/j.ijrmms.2023.105439. [28] YAN C Z, LUO Z Q, ZHENG Y C, et al. A 2D discrete moisture diffusion model for simulating desiccation fracturing of soil [J]. Engineering Analysis with Boundary Elements, 2022, 138: 42–64. DOI: 10.1016/j.enganabound.2022.02.006. [29] YAN C Z, WANG T, KE W H, et al. A 2D FDEM-based moisture diffusion-fracture coupling model for simulating soil desiccation cracking [J]. Acta Geotechnica, 2021, 16(8): 2609–2628. DOI: 10.1007/s11440-021-01297-4. [30] YAN C Z, FAN H W, HUANG D R, et al. A 2D mixed fracture-pore seepage model and hydromechanical coupling for fractured porous media [J]. Acta Geotechnica, 2021, 16(10): 3061–3086. DOI: 10.1007/s11440-021-01183-z. [31] OÑATE E, ROJEK J. Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems [J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(27/28/29): 3087–3128. DOI: 10.1016/j.cma.2003.12.056. [32] YAN C Z, ZHAO Z H, YANG Y, et al. A three-dimensional thermal-hydro-mechanical coupling model for simulation of fracturing driven by multiphysics [J]. Computers and Geotechnics, 2023, 155: 105162. DOI: 10.1016/j.compgeo.2022.105162. [33] YAN C Z, MA H, TANG Z C, et al. A two-dimensional moisture diffusion continuous model for simulating dry shrinkage and cracking of soil [J]. International Journal of Geomechanics, 2022, 22(10): 04022172. DOI: 10.1061/(ASCE)GM.1943-5622.0002570. [34] YAN C Z, ZHENG H, SUN G H, et al. Combined finite-discrete element method for simulation of hydraulic fracturing [J]. Rock Mechanics and Rock Engineering, 2016, 49(4): 1389–1410. DOI: 10.1007/s00603-015-0816-9. [35] LISJAK A, TATONE B S A, MAHABADI O K, et al. Hybrid finite-discrete element simulation of the EDZ formation and mechanical sealing process around a microtunnel in opalinus clay [J]. Rock Mechanics and Rock Engineering, 2016, 49(5): 1849–1873. DOI: 10.1007/s00603-015-0847-2. [36] WANG T, YAN C Z, HAN D, et al. Insights into the breaking mechanism and fragment pattern of soft rock assisted by free face under TBM wedge cutter indentation [J]. Engineering Fracture Mechanics, 2023, 291: 109580. DOI: 10.1016/j.engfracmech.2023.109580. [37] WANG T, YAN C Z, ZHENG H, et al. Optimum spacing and rock breaking efficiency of TBM double disc cutters penetrating in water-soaked mudstone with FDEM [J]. Tunnelling and Underground Space Technology, 2023, 138: 105174. DOI: 10.1016/j.tust.2023.105174. [38] FUKUDA D, NIHEI E, CHO S H, et al. Development of a numerical simulator for 3-D dynamic fracture process analysis of rocks based on hybrid FEM-DEM using extrinsic cohesive zone model [J]. Materials Transactions, 2020, 61(9): 1767–1774. DOI: 10.2320/matertrans.Z-M2020833. [39] DENG P H, LIU Q S, HUANG X, et al. Sensitivity analysis of fracture energies for the combined finite-discrete element method (FDEM) [J]. Engineering Fracture Mechanics, 2021, 251: 107793. DOI: 10.1016/j.engfracmech.2021.107793. [40] ZUO T, LI X L, WANG J G, et al. Insights into natural tuff as a building material: effects of natural joints on fracture fractal characteristics and energy evolution of rocks under impact load [J]. Engineering Failure Analysis, 2024, 163: 108584. DOI: 10.1016/j.engfailanal.2024.108584. -
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