Preparation method for transparent rock-like specimens with mechanic-controllable property: porosity strategy and its effect
ZHOU Yu1, 2, MA Xiyang1, YU Shuyang3, HAN Guansheng1, TANG Qiongqiong1, LI Bo4, WU Faquan1, 2
(1. State Key Laboratory of Intelligent Deep Metal Mining and Equipment, Shaoxing University, Shaoxing, Zhejiang 312000, China; 2. International Joint Laboratory of Digital Geotechnical and Intelligent Exploration, Shaoxing University, Shaoxing, Zhejiang 312000, China; 3. School of Transportation and Civil Engineering, Nantong University, Nantong, Jiangsu 226019, China;
4. School of Civil Engineering, Tongji University, Shanghai 200092, China)
Abstract：Inspired by the fundamental principle that inherent defects, such as primary pores and fractures in natural rocks, significantly influence their mechanical properties, this paper introduces the Mechanic-Controlled Sampling via Structure-Driven Design (MSSD) method for fabricating transparent rock-like samples with controllable mechanical characteristics. Utilizing this method, we fabricated intact and pre-fissured transparent rock-like samples with varying porosities (0%, 3%, 6%, 10%, 20%, and 30%). We established quantitative relationships between porosity and key mechanical parameters, including uniaxial compressive strength, elastic modulus, tensile strength, brittleness, cohesion, and internal friction angle. The influence mechanism of pores on crack propagation was elucidated through Franc3D simulations. Experimental results from intact samples demonstrate that the failure modes are highly consistent with those observed in natural rocks, allowing for clear observation and capture of the crack propagation process. As porosity increases, the various mechanical parameters of intact samples exhibit a linear decreasing trend, transitioning from hard rock-like material to soft rock-like material. Experimental results from pre-fissured samples indicate that increasing porosity leads to heightened surface roughness of wing cracks in single-fissure samples. In double-fissure samples, the rock bridge coalescence mode shifts from global to local coalescence, with the stress intensity factor KIII at the crack tip gradually decreasing, while the fracture mode in the rock bridge area transitions from tensile to shear type. Moreover, an increase in porosity correlates with a reduction in the number of petal-shaped cracks observed in all pre-fissured samples.
[1] 朱 磊，刘治成，刘成勇，等. 基于孔隙率和粒径的煤矸石力学性能预测试验研究[J]. 西安科技大学学报，2024，44(6)：1 083–1 094. (ZHU Lei，LIU Zhicheng，LIU Chengyong，et al. Experimental study on predicting the mechanical properties of coal gangue based on porosity and particle size[J]. Journal of Xi?an University of Science and Technology，2024，44(6)：1 083–1 094.(in Chinese))
[2] ZHAO H B，HU G L，LI W，et al. Research progress and thinking on the crack propagation law of pre-fractured rock[J]. Chinese Journal of Underground Space and Engineering，2016，12(Supp.2)：899–906.
[3] 张国凯，李海波，王明洋，等. 单裂隙花岗岩破坏强度及裂纹扩展特征研究[J]. 岩石力学与工程学报，2019，38(增1)：2 760–2 771. (ZHANG Guokai，LI Haibo，WANG Mingyang，et al. Research on the failure strength and crack propagation characteristics of single Crack Granite[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.1)：2 760–2 771.(in Chinese))
[4] 胡千庭，余长君，李全贵，等. 单轴压缩下裂隙砂岩宏细观损伤破坏特性的试验研究[J]. 实验力学，2025，40(1)：49–60.(HU Qianting，YU Changjun，LI Quangui，et al. Experimental study on macroscopic and microscopic damage and failure characteristics of fractured sandstone under uniaxial compression[J]. Experimental Mechanics，2025，40(1)：49–60.(in Chinese))
[5] 赵乾百，杨天鸿，张 兵，等. 不同裂隙倾角下岩石破坏模式及声发射特征[J]. 矿业科学学报，2025，10(2)：203–213.(ZHAO Qianbai，YANG Tianhong，ZHANG Bing，et al. Rock failure modes and acoustic emission characteristics under different fracture angles[J]. Journal of Mining Science，2025，10(2)：203–213.(in Chinese))
[6] 李东杰，王帅旗，曹 阔. 单轴作用下岩石的破坏行为及声发射响应特征研究[J]. 煤，2025，34(1)：27–31.(LI Dongjie，WANG Shuaiqi，CAO Kuo. Study on the failure behavior and acoustic emission response characteristics of rocks under uniaxial action[J]. Coal，2025，34(1)：27–31.(in Chinese))
[7] 刘 强，吴荆凯，胡文韬，等. 水泥基3D打印技术在岩石力学教学实验中的应用[J]. 实验技术与管理，2024，41(9)：199–205.(LIU Qiang，WU Jingkai，HU Wentao，et al. Application of cement-based 3D printing technology in rock mechanics teaching experiments[J]. Experimental Technology and Management，2024，41(9)：199–205. (in Chinese))
[8] 刘志浩. 水泥砂浆试件及风化片麻岩的力学性能关系研究[硕士学位论文][D]. 山东：山东农业大学，2013.(LIU Zhihao. Study on the relationship between mechanical properties of cement mortar specimens and weathered gneiss[M. S. Thesis][D]. Shandong：Shandong Agricultural University，2013.(in Chinese))
[9] NAN Q，HONGWEI W，YONGYAN W. Study of experiment on rock-like material consist of fly-ash，cement and mortar[J]. Conference Series Earth and Environmental Science，2018，128(1)：1–6.
[10] WANG H C，LIU K，LUKIC B，et al. In-situ deformation and fracturing characteristics of geomaterials under dynamic loading：insights from ultra-high-speed X-ray phase contrast imaging and DEM modelling[J]. International Journal of Rock Mechanics and Mining Sciences，2024，175：1–22.
[11] SHAO Y，YANG J，KIM J，et al. Microscopic analysis of mechanical anisotropy and damage evolution of 3D printed rock-like samples under uniaxial compressive tests[J]. Journal of Rock Mechanics and Geotechnical Engineering，2025，17(2)：688–704.
[12] 何风贞，李桂臣，阚甲广，等. 岩石多尺度损伤研究进展[J]. 煤炭科学技术，2024，52(10)：33–53.(HE Fengzhen，LI Guichen，KAN Jiaguang，et al. Research progress on multi-scale damage of rocks[J]. Coal Science and Technology，2024，52(10)：33–53.(in Chinese))
[13] QIU B，HAN T，LIU Y. Application and study of epoxy resin AB adhesive in the preparation of rock thin section[J]. Journal of Physics：Conference Series，2023，2499(1)：1–7.
[14] FU J W，LIU S L，ZHU W S，et al. Experiments on failure process of new rock-like specimens with two internal cracks under biaxial loading and the 3-D simulation[J]. Acta Geotechnica，2018，13(4)：853–867.
[15] 葛进进. 初始应力状态下岩石爆破裂纹扩展的模型试验研究[博士学位论文][D]. 淮南：安徽理工大学，2020.(GE Jinjin. Model experimental study on rock blasting crack propagation under initial stress state[Ph. D. Thesis][D]. Huainan：Anhui University of Science and Technology，2020.(in Chinese))
[16] 张腊梅，曾 强，何 贵，等. 环氧树脂AB胶制作岩石薄片的优化研究[J]. 四川建材，2024，50(4)：238–240.(ZHANG Lamei，ZENG Qiang，HE Gui，et al. Optimization study on the production of rock flakes using epoxy resin AB adhesive[J]. Sichuan Building Materials，2024，50(4)：238–240.(in Chinese))
[17] 任誉茜. 基于透明类岩石材料的层状围岩隧道力学特性研究[硕士学位论文][D]. 重庆：重庆交通大学，2024.(REN Yuqian. Research on the mechanical properties of layered surrounding rock tunnels based on transparent rock materials[M. S. Thesis][D]. Chongqing：Chongqing Jiaotong University，2024.(in Chinese))
[18] 付金伟，朱维申，曹冠华，等. 岩石中三维单裂隙扩展过程的试验研究和数值模拟[J]. 煤炭学报，2013，38(3)：411–417.(FU Jinwei，ZHU Weishen，CAO Guanhua，et al. Experimental study and numerical simulation of three-dimensional single fracture propagation process in rocks[J]. Journal of China Coal Society，2013，38(3)：411–417.(in Chinese))
[19] ADAMS M，SINES G. Crack extension from flaws in a brittle material subjected to compression[J]. Tectonophysics，1978，49(1/2)：97–118.
[20] 晏 敏，邓金根，田得粮，等. 环氧树脂胶结人造砂岩单轴力学性质研究[J]. 石油科学通报，2023，8(5)：600–613.(YAN Min，DENG Jingen，TIAN Deliang，et al. Research on the uniaxial mechanical properties of epoxy resin bonded artificial sandstone[J]. Petroleum Science Bulletin，2023，8(5)：600–613.(in Chinese))
[21] 朱珍德，林恒星，孙亚霖. 透明类岩石内置三维裂纹扩展变形试验研究[J]. 岩土力学，2016，37(4)：913–921.(ZHU Zhende，LIN Xingxing，SUN Yalin. Experimental study on three-dimensional crack propagation and deformation inside transparent rocks[J]. Rock and Soil Mechanics，2016，37(4)：913–921.(in Chinese))
[22] 郭东明，刘嘉华，杨 静，等. 基于环氧树脂固化法的类岩石材料配比研究[J]. 实验力学，2025，40(1)：115–124.(GUO Dongming，LIU Jiahua，YANG Jing，et al. Research on the proportion of rock like materials based on epoxy resin curing method[J]. Experimental Mechanics，2025，40(1)：115–124.(in Chinese))
[23] 付金伟. 含三维裂隙试件在双轴压力和水压作用下压裂试验与数值模拟研究[博士学位论文][D]. 济南：山东大学，2015.(FU Jinwei. Research on fracturing test and numerical simulation of three dimensional fracture specimens under biaxial pressure and water pressure[Ph. D. Thesis][D]. Jinan：Shandong University，2015.(in Chinese))
[24] 李元海，林志斌，秦先林，等. 透明岩体相似材料物理力学特性研究[J]. 中国矿业大学学报，2015，44(6)：977–982.(LI Yuanhai，LIN Zhibin，QIN Xianlin，et al. Study on the physical and mechanical properties of similar materials in transparent rock mass[J]. Journal of China University of Mining and Technology，2015，44(6)：977–982.(in Chinese))
[25] 叶 伟. 透明脆性岩石相似材料内置三维裂纹扩展试验研究[硕士学位论文][D]. 重庆：重庆大学，2016.(YE Wei. Experimental study on three-dimensional crack propagation in transparent brittle rock like materials[M. S. Thesis][D]. Chongqing：Chongqing University，2016.(in Chinese))
[26] 朱语聪. 透明硬岩相似材料物理力学特性试验及应用研究[硕士学位论文][D]. 重庆：重庆交通大学，2022.(ZHU Yucong. Experimental and applied study on physical and mechanical properties of transparent hard rock similar materials[M. S. Thesis][D]. Chongqing：Chongqing Jiaotong University，2022.(in Chinese))
[27] 刘善军，吴立新. 脆性岩石与有机玻璃受力红外辐射特征的比较[J]. 岩石力学与工程学报，2007，26(增2)：4 183–4 188.(LIU Shanjun，WU Lixin. Comparison of infrared radiation characteristics under stress between brittle rocks and organic glass[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(Supp.2)：4 183–4 188.(in Chinese))
[28] 陈 果. 三维币状裂纹扩展及贯通机制试验研究[硕士学位论文][D]. 重庆：重庆大学，2015.(CHEN Guo. Experimental study on the propagation and penetration mechanism of three-dimensional coin shaped cracks[M. S. Thesis][D]. Chongqing：Chongqing University，2015.(in Chinese))
[29] WONG R H C，LAW C M，CHAU K T，et al. Crack propagation from 3-D surface fractures in PMMA and marble specimens under uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences，2004，41(3)：361–366.
[30] ZHOU X P，FU L，JU W，et al. An experimental study of the mechanical and fracturing behavior in PMMA specimen containing multiple 3D embedded flaws under uniaxial compression[J]. Theoretical and Applied Fracture Mechanics，2019，101(13)：207–216.
[31] 胡南燕，黄建彬，罗斌玉，等. 透明岩石相似材料配比试验研究[J]. 煤炭科学技术，2023，51(6)：52–61.(HU Nanyan，HUANG Jianbin，LUO Binyu，et al. Experimental study on the proportion of similar materials in transparent rocks[J]. Coal Science and Technology，2023，51(6)：52–61.(in Chinese))
[32] 刘 蓓. 软硬互层透明相似岩体制备及力学特性试验研究[硕士学位论文][D]. 重庆：重庆交通大学，2023.(LIU Bei. Preparation and experimental study on mechanical properties of soft soft interlayer transparent similar rock mass[M. S. Thesis][D]. Chongqing：Chongqing Jiaotong University，2023.(in Chinese))
[33] 刘 蓓. 透明岩石单轴压缩力学特性研究[J]. 科技通报，2023，39(5)：102–107.(LIU Bei. Research on the uniaxial compression mechanical properties of transparent rock[J]. Science and Technology Bulletin，2023，39(5)：102–107.(in Chinese))
[34] 李元海，林志斌. 透明岩体相似物理模拟试验新方法研究[J]. 岩土工程学报，2015，37(11)：2 030–2 039.(LI Yuanhai， LIN Zhibin Research on a new method of physical simulation test for transparent rock mass similarity[J]. Journal of Geotechnical Engineering，2015，37(11)：2 030–2 039.(in Chinese))
[35] 李 兵. 岩石相似材料的试验研究[硕士学位论文][D]. 重庆：重庆大学，2015.(LI Bing. Experimental study on rock like materials[M. S. Thesis][D]. Chongqing：Chongqing University，2015.(in Chinese))
[36] DYSKIN A V，GERMANOVICH L N，JEWELL R J，et al. Some experimental results on three-dimensional crack propagation in compression[J]. Bulletin of the American Mathematical Society，1995，31(240)：1–10.
[37] FU J W，CHEN K，ZHU W，et al. Progressive failure of new modelling material with a single internal crack under biaxial compression and the 3-D numerical simulation[J]. Engineering Fracture Mechanics，2016，165(1)：140–152.
[38] 朱昌星，安烨明，李伟东. 单轴压缩下透明类岩石损伤演化特征研究[J]. 实验力学，2022，37(5)：701–710.(ZHU Changxing，AN Yeming，LI Weidong. Study on the damage evolution characteristics of transparent rock under uniaxial compression[J]. Experimental Mechanics，2022，37(5)：701–710.(in Chinese))
[39] 黄明利，黄凯珠. 三维表面裂纹相互作用扩展贯通机制试验研究[J]. 岩石力学与工程学报，2007，26(9)：1 794–1 799.(HUANG Mingli，HUANG Kaizhu. Experimental study on the propagation and penetration mechanism of three-dimensional surface crack interaction[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(9)：1 794–1 799. (in Chinese))
[40] GE J，XU Y. A method for making transparent hard rock‐like material and its application[J]. Advances in Materials Science and Engineering，2019，2019(1)：1–14.
[41] 毛华晋. 孔隙结构特征及其对岩石力学性能的影响分析[J]. 四川水泥，2020，(11)：320–321.(MAO Huajin. Analysis of pore structure characteristics and their influence on rock mechanical properties[J]. Sichuan Cement，2020，(11)：320–321.(in Chinese))
[42] ZHANG G K，LI H B，WANG M Y，et al. Study on characteristics of failure strength and crack propagation of granite rocks containing a single fissure[J]. Chinese Journal of Rock Mechanics and Engineering ，2019，38(1)：2 760–2 771.
[43] 余 宸，田 威，王 杰，等. 砂型3D打印材料在岩体物理模型试验中的应用研究及展望[J]. 材料导报，2024，38(12)：77–85.(YU Chen，TIAN Wei，WANG Jie，et al. Research and prospect on the application of sand mold 3D printing materials in rock physical model testing[J]. Materials Introduction，2024，38(12)：77–85.(in Chinese))
[44] 王修春，魏 军，伊希斌，等. 3D打印技术类型与打印材料适应性[J]. 信息技术与信息化，2014，(4)：84–86.(WANG Xiuchun，WEI Jun，YIN Xibin，et al. Types of 3D printing technology and adaptability of printing materials[J]. Information Technology and Informatization，2014，(4)：84–86.(in Chinese))
[45] 余雷雷，徐 颖，葛进进，等. 基于 3D 打印试件的裂隙岩体断裂特性及裂纹扩展特征研究[J]. 爆破，2024，41(4)：25–34.(YU Leilei，XU Ying，GE Jinjin，et al. Research on fracture characteristics and crack propagation characteristics of fractured rock mass based on 3D printed specimens[J]. Blasting，2024，41(4)：25–34.(in Chinese))
[46] 刘华博. 预制裂纹类岩石材料裂纹扩展规律及3D打印技术应用[博士学位论文][D]. 北京：中国矿业大学(北京)，2018.(LIU Huabo. Crack propagation law and 3D printing technology application of prefabricated crack type rock materials[Ph. D. Thesis][D]. Beijing：University of Mining and Technology(Beijing)，2018.(in Chinese))
[47] 王亚帆. 模拟煤岩体的3D打印材料及其应用[硕士学位论文][D]. 阜新：辽宁工程技术大学，2022.(WANG Yafan. 3D printing materials for simulating coal and rock masses and their applications[M. S. Thesis][D]. Fuxin：Liaoning University of Engineering and Technology，2022.(in Chinese))
[48] FU J W，LIU S，LI L，et al. A modelling resin material and its application in rock-failure study：Samples with two 3D internal fracture surfaces[J]. Open Geosciences，2020，12(1)：1 237–1 246.
[49] 邬爱清，赵 文. 长江科学院主持修编的国标《工程岩体分级标准》GB/T50218—2014正式发布[J]. 长江科学院院报，2015，32(1)：124.(WU Aiqing，ZHAO Wen. The national standard“Engineering Rock Mass Classification Standard” GB/T50218—2014，revised by the Yangtze River Academy of Sciences，has been officially released[J]. Journal of the Yangtze River Academy of Sciences，2015，32(1)：124.(in Chinese))
[50] MENG F，WONG L N Y，ZHOU H. Rock brittleness indices and their applications to different fields of rock engineering：A review[J]. Journal of Rock Mechanics and Geotechnical Engineering，2021，13(1)：221–247.
[51] GONG Q M，ZHAO J. Influence of rock brittleness on TBM penetration rate in Singapore granite[J]. Tunnelling and Underground Space Technology，2007，22(3)：317–324.
[52] SINGH S P. Brittleness and the mechanical winning of coal[J]. Mining Science and Technology，1986，3(3)：173–180.
[53] CAI M F. Prediction and prevention of rockburst in metal mines-A case study of Sanshandao gold mine[J]. Journal of Rock Mechanics and Geotechnical Engineering，2016，8(2)：204–211.
[54] MOHAMMADI S D，TORABI-KAVEH M，BAYATI M. Prediction of TBM penetration rate using intact and mass rock properties(case study：Zagros long tunnel，Iran)[J]. Arabian Journal of Geosciences，2015，8(6)：3 893–3 904.
[55] 贾喜荣，刘跃东，刘 畅，等. 基于岩石单轴抗压强度和抗拉强度的非线性Coulomb强度准则[J]. 岩石力学与工程学报，2025，44(增1)：1–9.(JIA Xirong，LIU Yuedong，LIU Chang，et al. Nonlinear Coulomb strength criterion based on uniaxial compressive strength and tensile strength of rocks[J]. Chinese Journal of Rock Mechanics and Engineering，2025，44(Supp.1)：1–9.(in Chinese))
[56] 贾喜荣，冯秋喜. Coulomb准则与Griffith Mohr准则的一致性及其应用[J]. 太原理工大学学报，1998，(5)：26–28.(JIA Xirong，FENG Qiuxi. Consistency and application of Coulomb criterion and Griffith Mohr criterion[J]. Journal of Taiyuan University of Technology，1998，(5)：26–28.(in Chinese))
[57] 赵 坚，李海波. 莫尔–库仑和霍克–布朗强度准则用于评估脆性岩石动态强度的适用性[J]. 岩石力学与工程学报，2003，22(2)：171–176.(ZHAO Jian，LI Haibo. The applicability of Mohr Coulomb and Hooke Brown strength criteria for evaluating the dynamic strength of brittle rocks[J]. Chinese Journal of Rock Mechanics and Engineering，2003，22(2)：171–176.(in Chinese))
[58] 余 宸，田 威，云 伟，等. 3D打印类岩石试样材料相似度定量评价方法及其脆性特征[J]. 中南大学学报：自然科学版，2025，56(5)：1 969–1 980.(YU Chen，TIAN Wei，YUN Wei，et al. Quantitative evaluation method for material similarity and brittleness characteristics of 3D printed rock samples[J]. Journal of Central South University：Natural Science，2025，56(5)：1 969–1 980.(in Chinese))
[59] 余洋林，许江波，费东阳，等. 花岗岩单轴压缩力学特性试验及数值模拟[J]. 桂林理工大学学报，2022，42(1)：85–92.(YU Yanglin，XU Jiangbo，FEI Dongyang，et al. Experimental and numerical simulation of uniaxial compression mechanical properties of granite[J]. Journal of Guilin University of Technology，2022，42(1)：85–92.(in Chinese))
[60] 张沛远. 岩石直接拉伸与巴西劈裂抗拉强度差异特征及其影响机制研究[博士学位论文][D]. 武汉：武汉大学，2024.(ZHANG Peiyuan. Research on the difference characteristics and influence mechanism of direct tensile and Brazilian splitting tensile strength of rocks[Ph. D. Thesis][D]. Wuhan：Wuhan University，2024.(in Chinese))
[61] 陈 骏. 动载作用下岩石强度的极限分析[博士学位论文][D]. 北京：中国矿业大学(北京)，2017.(CHEN Jun. Limit analysis of rock strength under dynamic loading[Ph. D. Thesis][D]. Beijing：China University of Mining and Technology(Beijing)，2017.(in Chinese))
[62] GONG F，ZHANG L，WANG S. Loading rate effect of rock material with the direct tensile and three Brazilian disc tests[J]. Advances in Civil Engineering，2019，2019(1)：1–8.
[63] 张国森. 不同风化程度灰岩强度劣化特征及损伤模型[硕士学位论文][D]. 阜新：辽宁工程技术大学，2024.(ZHANG Guosen. Characteristics of strength degradation and damage model of limestone with different degrees of weathering[M. S. Thesis][D]. Fuxin：Liaoning Technical University，2024.(in Chinese))
[64] 史文兵，李 华，王小明，等. 单轴压缩条件下溶蚀岩体力学特性数值试验研究[J]. 应用力学学报，2023，40(5)：1 143–1 153.(SHI Wenbing，LI Hua，WANG Xiaoming，et al. Numerical experimental study on mechanical properties of dissolved rock mass under uniaxial compression conditions[J]. Journal of Applied Mechanics，2023，40(5)：1 143–1 153.(in Chinese))
[65] 刘 刚，李英明，肖福坤，等. 单、三轴及孔隙水作用下黄砂岩破坏力学行为及损伤演化规律研究[J]. 岩石力学与工程学报，2019，38(增2)：3 532–3 544.(LIU Gang，LI Yingming，XIAO Fukun，et al. Research on the mechanical behavior and damage evolution of yellow sandstone under uniaxial，triaxial，and pore water effects[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.2)：3 532–3 544.(in Chinese))
[66] 杨圣奇，刘相如，李玉寿. 单轴压缩下含孔洞裂隙砂岩力学特性试验分析[J]. 岩石力学与工程学报，2012，31(增2)：3 539–3 546. (YANG Shengqi，LIU Xiangru，LI Yushou. Experimental analysis of mechanical properties of sandstone with pores and fractures under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(Supp.2)：3 539–3 546.(in Chinese))
[67] 张志镇，高 峰. 单轴压缩下红砂岩能量演化试验研究[J]. 岩石力学与工程学报，2012，31(5)：953–962.(ZHANG Zhizhen，GAO Feng. Experimental study on energy evolution of red sandstone under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(5)：953–962.(in Chinese))
[68] 唐 宇，阳军生，郑响凑，等. 高温富水隧道弱风化片麻岩力学特性试验研究[J]. 岩石力学与工程学报，2025，44(1)：128–139. (TANG Yu，YANG Junsheng，ZHENG Xiangcuo，et al. Experimental study on mechanical properties of weakly weathered gneiss in high-temperature rich water tunnel[J]. Chinese Journal of Rock Mechanics and Engineering，2025，44(1)：128–139.(in Chinese))
[69] 班宇鑫，傅 翔，谢 强，等. 页岩巴西劈裂裂缝形态评价及功率谱特征分析[J]. 岩土工程学报，2019，41(12)：2 307–2 315.(BAN Yuxin，FU Xiang，XIE Qiang，et al. Evaluation of shale Brazilian splitting fracture morphology and power spectrum characteristics analysis[J]. Chinese Journal of Geotechnical Engineering，2019，41(12)：2 307–2 315.(in Chinese))
[70] 徐浩淳，金爱兵，赵怡晴，等. 热处理砂岩不同接触角巴西劈裂数值模拟研究[J]. 岩土力学，2022，43(增2)：588–597.(XU Haochun，JIN Aibing，ZHAO Yiqing，et al. Numerical simulation study on Brazilian splitting at different contact angles of heat-treated sandstone[J]. Rock and Soil Mechanics，2022，43(Supp.2)：588–597.(in Chinese))
[71] GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical transactions of the royal society of london. Series A，containing papers of a mathematical or physical character，1921，221(582/593)：163–198.
[72] DYSKIN A V，SAHOURYEH E，JEWELL R J，et al. Influence of shape and locations of initial 3-D cracks on their growth in uniaxial compression[J]. Engineering Fracture Mechanics，2003，70(15)：2 115–2 136.
[73] WONG R H C，HUANG M L，JIAO M R，et al. The mechanisms of crack propagation from surface 3-D fracture under uniaxial compression[J]. Key Engineering Materials，2004，488(261/263)：219–224.
[74] 王海军，张九丹，任 然，等. 基于3D-ILC含不同角度内裂纹圆盘断裂特性研究[J]. 岩土工程学报，2019，41(9)：1 636–1 644. (WANG Haijun，ZHANG Jiudan，REN Ran，et al. Research on the fracture characteristics of circular discs with internal cracks at different angles based on 3D-ILC[J]. Chinese Journal of Geotechnical Engineering，2019，41(9)：1 636–1 644.(in Chinese))
[75] 王海军，李汉章，任 然，等. 基于3D-ILC三点弯脆性固体内裂纹扩展规律及破坏特征研究[J]. 岩石力学与工程学报，2019，38(12)：2 463–2 477.(WANG Haijun，LI Hanzhang，REN Ran，et al. Research on the propagation law and failure characteristics of internal cracks in brittle solids based on 3D-ILC three-point bending[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(12)： 2 463–2 477.(in Chinese))
[76] 艾书民，于 明，成晓鸣，等. 基于Franc3D软件的三维裂纹扩展分析与应用[J]. 机械强度，2018，40(1)：251–254.(AI Shumin，YU Ming，CHENG Xiaoming，et al. Three dimensional crack propagation analysis and application based on Franc3D software[J]. Mechanical Strength，2018，40(1)：251–254.(in Chinese))
2025, Vol. 44 
