(1. Department of Civil Engineering，Tsinghua University，Beijing 100084，China；2. Institute of Deep Earth Sciences and Green Energy，Shenzhen University，Shenzhen，Guangdong 518060，China；3. Guangdong Provincial Key Laboratory of Deep Earth Sciences and Geothermal Energy Exploitation and Utilization，Shenzhen University，Shenzhen，Guangdong 518060，China；
4. CNPC Engineering Technology R&D Co.，Ltd.，Beijing 102206，China)
Abstract：Fracture behaviors of rock samples with discontinuities is difficult to quantify and predict. In this study，machine learning method is used to predict mode I fracture toughness and crack propagation mode of rock samples with an infilled fracture. Firstly，the feasibility of the method was verified by comparison of results of notched semi-circle bend test and numerical simulation based on discrete element method，and the dataset which filtered the outliers was generated by a lot of random numerical simulations. Multiple techniques were used in the preprocessing of dataset. Then four classical machine learning models were established. The optimal parameters of the models were obtained by grid search and five-fold cross-validation method. Multiple indicators and graphs were used to verify the prediction performances of the models. Comparison between the four models shows that Multilayer Perceptron(MLP) is the optimal machine learning model. The sensitivity of the MLP model was analyzed and the stability is good. The MLP model was applied to the test samples，which has high prediction accuracy. And a user interface program was developed. The data driven model of rock mechanics based on the machine learning method reduces time cost compared with the traditional test and numerical simulation，which provides a new method and thought for solving traditional rock engineering problems.
陈进帆1，尚德磊1，2，3，赵志宏1，陈朝伟4. 基于机器学习的含充填裂隙岩样断裂行为预测方法[J]. 岩石力学与工程学报, 2023, 42(S1): 3458-3472.
CHEN Jinfan1，SHANG Delei1，2，3，ZHAO Zhihong1，CHEN Zhaowei4. Prediction method of fracture behaviors of rock samples with an infilled fracture based on machine learning. , 2023, 42(S1): 3458-3472.
[1] 张 盛，李小军，李大伟. 岩石I型断裂韧度测试技术和理论研究综述[J]. 河南理工大学学报：自然科学版，2009，28(1)：33–38. (ZHANG Sheng，LI Xiaojun，LI Dawei. A review of test technique and theory of mode I rock fracture toughness[J]. Journal of Henan Polytechnic university：Natural Science，2009，28(1)：33–38.(in Chinese))
[2] 包 含，伍法权，郗鹏程. 岩石I型断裂韧度估算及其影响因素分析[J]. 煤炭学报，2017，42(3)：604–612. (BAO Han，WU Faquan，XI Pengcheng. Estimation of mode I fracture toughness of rock and its impact factors analysis[J]. Journal of China Coal Society，2017，42(3)：604–612.(in Chinese))
[3] 包 含，郭文明，张国彪，等. 基于强度参数脆性指数的岩石I型断裂韧度评价[J]. 建筑科学与工程学报，2018，35(4)：97–104. (BAO Han，GUO Wenming，ZHANG Guobiao，et al. Evaluation of mode I fracture toughness of rock based on brittleness index of strength parameters[J]. Journal of Architecture and Civil Engineering，2018，35(4)：97–104.(in Chinese))
[4] KURUPPU M D，OBARA Y，AYATOLLAHI M R，et al. ISRM- suggested method for determining the mode I static fracture toughness using semi-circular bend specimen[J]. Rock Mechanics and Rock Engineering，2014，47(1)：267–274.
[5] 衡 帅，杨春和，郭印同，等. 层理对页岩水力裂缝扩展的影响研究[J]. 岩石力学与工程学报，2015，34(2)：228–237.(HENG Shuai，YANG Chunhe，GUO Yintong，et al. Influence of bedding planes on hydraulic fracture propagation in shale formations[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(2)：228–237.(in Chinese))
[6] 李 斌，黄 达，姜清辉，等. 层理方向对砂岩断裂模式及韧度的影响规律试验研究[J]. 岩土工程学报，2019，41(10)：1 854–1 862. (LI Bin，HUANG Da，JIANG Qinghui，et al. Fracture Pattern and Toughness of Layered Sandstone influenced by layer orientation[J]. Chinese Journal of Geotechnical Engineering，2019，41(10)：1 854– 1 862.(in Chinese))
[7] 吴秋红，谢成龙，谢柚生，等. 基于非对称半圆弯曲试件(ASCB)测定花岗岩的Ⅰ/Ⅱ断裂力学行为[J]. 中南大学学报：英文版，2022，29(4)：1 289–1 304.(WU Qiuhong，XIE Chenglong，XIE Yousheng，et al. Extending application of asymmetric semi-circular bend specimen to investigate mixed mode I/II fracture behavior of granite[J]. Journal of Central South University，2022，29(4)：1 289–1 304.(in Chinese))
[8] 陈彦安，卞 康，刘 建，等. 非对称载荷下各向异性砂岩半圆弯曲断裂特性的离散元研究[J]. 岩石力学与工程学报，2021，40(7)：1 412–1 427.(CHEN Yan?an，BIAN Kang，LIU Jian，et al. Granular discrete element research on semi-circular bending fracture characteristics of anisotropic sandstone under asymmetric loading[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(7)：1 412–1 427.(in Chinese))
[9] 李江腾，王慧文，林 杭. 横观各向同性板岩层理角度与抗压强度及断裂韧度的相关规律[J]. 湖南大学学报：自然科学版，2016，43(7)：126–131.(LI Jiangteng，WANG Huiwen，LIN Hang. Relationship among stratification angle，compressive strength，and fracture toughness of transversely isotropic slate[J]. Journal of Hunan University：Natural Science，2016，43(7)：126–131.(in Chinese))
[10] 蔺海晓，钱立振，程 龙，等. 层状千枚岩的断裂特性[J]. 高压物理学报，2021，35(5)：115–126.(LIN Haixiao，QIAN Lizhen，CHENG Long，et al. Fracture characteristics of layered phyllite[J]. Chinese Journal of High Pressure Physics，2021，35(5)：115–126.(in Chinese))
[11] LEE H P，OLSON J E，HOLDER J，et al. The interaction of propagating opening mode fractures with preexisting discontinuities in shale[J]. Journal of Geophysical Research：Solid Earth，2015，120(1)：169–181.
[12] LIU Z N，XU H R，ZHAO Z H，et al. DEM modeling of interaction between the propagating fracture and multiple pre-existing cemented discontinuities in shale[J]. Rock Mechanics and Rock Engineering，2019，52(6)：1 993–2 001.
[13] 李二强，张龙飞，赵宁宁，等. 风化作用下层状板岩I型断裂特性试验研究[J]. 中南大学学报：自然科学版，2022，53(4)：1 406– 1 415.(LI Erqiang，ZHANG Longfei，ZHAO Ningning，et al. Experimental investigation on mode I fracture behaviors oflayered slate under condition of air-weathering[J]. Journal of Central South University：Science and Technology，2022，53(4)：1 406–1 415.(in Chinese))
[14] 李二强，冯吉利，朱天宇，等. 基于数字图像相关方法的层状板岩I型断裂特性研究[J]. 采矿与安全工程学报，2021，38(5)：979–987.(LI Erqiang，FENG Jili，ZHU Tianyu，et al. Examining type I fracture characteristics in layered slates with digital image correlation[J]. Journal of Mining and Safety Engineering，2021，38(5)：979–987.(in Chinese))
[15] 陈立超，王生维，张典坤. 层理方位对致密砂岩断裂行为影响及其压裂意义[J]. 地下空间与工程学报，2021，17(增2)：689–695. (CHEN Lichao，WANG Shengwei，ZHANG Diankun. Influence of bedding orientation on fracture behavior of tight sandstone and its fracturing significance[J]. Chinese Journal of Underground Space and Engineering，2021，17(Supp.2)：689–695.(in Chinese))
[16] XING L，CHRISTOS E，ATHANASIOU，et al. A machine learning approach to fracture mechanics problems[J]. Acta Materialia，2020，190：105–112.
[17] ALIPOUR M，ESATYANA E，SAKHAEE POUR A，et al. Characterizing Fracture Toughness Using Machine Learning[J]. Journal of Petroleum Science and Engineering，2021，200：108202.
[18] DAGHIGH V，LACY T E，DAGHIGH H，et al. Machine learning predictions on fracture toughness of multiscale bio-nano- composites[J]. Journal of Reinforced Plastics and Composites，2020，39(15/16)：587–598.
[19] WANG Y T，ZHANG X，LIU X S. Machine learning approaches to rock fracture mechanics problems：Mode-I fracture toughness determination[J]. Engineering Fracture Mechanics，2021，253：107890.
[20] 谭 攀，饶秋华，李 卓，等. 考虑断裂韧度的PFC3D细观参 数标定新方法[J]. 中南大学学报：自然科学版，2021，52(8)： 2 849–2 866.(TAN Pan，RAO Qiuhua，LI Zhuo，et al. A new method for quantitative determination of PFC3D microscopic parameters considering fracture toughness[J]. Journal of Central South University：Science and Technology，2021，52(8)：2 849–2 866.(in Chinese))
[21] 石 崇，张 强，王盛年. 颗粒流(PFC 5.0)数值模拟技术及应用[M]. 北京：中国建筑工业出版社，2018：1–60.(SHI Chong，ZHANG Qiang，WANG Shengnian. Numerical simulation technology and application with particle flow code(PFC 5.0)[M]. Beijing：China Architecture and Building Press，2018：1–60.(in Chinese))
[22] 姜兆华，林山泉. 单裂隙岩体单轴压缩颗粒流数值模拟[J]. 建筑结构，2018，48(增2)：940–943.(JIANG Zhaohua，LIN Shanquan. Numerical simulation of a single pre-crack rock under uniaxial compression using PFC simulation[J]. Building Structure，2018，48(Supp.2)：940–943.(in Chinese))
[23] 赵晓康，董 侨，陈雪琴，等. 考虑初始缺陷的水泥基复合材料细观开裂研究[J]. 中国公路学报，2020，33(10)：230–239.(ZHAO Xiaokang，DONG Qiao，CHEN Xueqin，et al. Mesoscale cracking of cement-treated composites with initial defects[J]. China Journal of Highway and Transport，2020，33(10)：230–239.(in Chinese))
[24] 张 琰，李江腾. 单调及循环加载下大理岩断裂特性研究[J]. 岩石力学与工程学报，2019，38(增2)：3 313–3 320.(ZHANG Yan，LI Jiangteng. Study on fracture characteristics of marble under monotone and cyclic loading[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.2)：3 313–3 320.(in Chinese))
[25] 崔振东，刘大安，安光明，等. 岩石I型断裂韧度测试方法研究进展[J]. 测试技术学报，2009，23(3)：189–196.(CUI Zhendong，LIU Daan，AN Guangming，et al. Research progress in mode-I fracture toughness testing methods for rocks[J]. Journal of Test and Measurement Technology，2009，23(3)：189–196.(in Chinese))
[26] 李 斌，黄 达，马文著. 层理面特性对砂岩断裂力学行为的影响研究[J]. 岩土力学，2020，41(3)：858–868.(LI Bin，HUANG Da，MA Wenzhu. Study on the influence of bedding plane on fracturing behavior of sandstone[J]. Rock and Soil Mechanics，2020，41(3)：858–868.(in Chinese))
[27] 汤志立，徐千军. 基于9种机器学习算法的岩爆预测研究[J]. 岩石力学与工程学报，2020，39(4)：773–781.(TANG Zhili，XU Qianjun. Rockburst prediction based on nine machine learning algorithms[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(4)：773–781.(in Chinese))
2023, Vol. 42 
