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| Granular discrete element research on semi-circular bending fracture characteristics of anisotropic sandstone under asymmetric loading |
| CHEN Yanan1,2,BIAN Kang1,2,LIU Jian1,2,CUI Deshan3,LI Yiran3 |
| (1. State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,Hubei 430071,China;2. University of Chinese Academy of Sciences,Beijing 100049,China;3. Faculty of Engineering,China University of Geosciences(Wuhan),Wuhan,Hubei 430074,China) |
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Abstract Reservoir resources often occur in anisotropic jointed rock mass and fracture mode of anisotropic reservoirs is relatively complex,which make it difficult to carry out efficient exploitation only based on engineering experiences. To better understand the fracture characteristics of anisotropic reservoirs,to realize the control and prediction of fracture expansion morphology,and hence,to collect reservoirs more scientifically,this paper uses the discrete element method(DEM) to study fracture characteristics of the anisotropic sandstone by semi-circular bending test under asymmetric loading. By adjusting the asymmetric degree of the bottom bearing, the control of rock mass fracture from pure I mode to pure II mode can be achieved. The main results are as follows:(1) The peak load of the semi-circular bending samples shows obvious anisotropy,showing distribution forms of “W” and “increasing-stable-increasing” with increasing the joint angle,and a trend of “precipitous drop-stable” with increasing the asymmetric coefficient. (2) SCB samples with different notch angles and joint distributions show different failure modes mainly including offset type,bedding type,cut-bedding type and composite bedding type. With increasing the asymmetric coefficient,the stress field in the samples changes,making fracture path of the samples deviate along the movement direction of the bearing. (3) The fracture toughness of the samples obtained by solving the geometric factor,which is obtained based on the calculation of J-integral and by which 3 kinds of asymmetric loading ways of pure II mode,pure I mode and compound mode are designed,shows obvious anisotropy with the change of the joint angle and presents a trend of “precipitous drop and stable” with increasing the asymmetric coefficient. (4) Impacted by the joints,the initial crack angles of pure I mode and pure II mode are respectively distributed in the range of 0°–36.9°and 47.68°–76.12°,which are not exactly the same as the theoretical values.
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[1] 于兴河. 碎屑岩系油气储层沉积学[M]. 2版. 北京:石油工业出版社,2008:379–380.(YU Xinghe. Sedimentology of oil and gas reservoirs in the clastic series[M]. 2nd ed. Beijing:Petroleum Industry Press,2008:379–380.(in Chinese))
[2] 孙广忠. 论“岩体结构控制论”[J]. 工程地质学报,1993,1(1):14–18.(SUN Guangzhong. On “rock mass structure cybernetics”[J]. Journal of Engineering Geology,1993,1(1):14–18.(in Chinese))
[3] 刘佑荣,唐辉明. 岩体力学[M]. 北京:化学工业出版社,2008:56–58.(LIU Yourong,TANG Huiming. Rock mechanics[M]. Beijing:Chemical Industry Press,2008:56–58.(in Chinese))
[4] 彪仿俊. 水力压裂水平裂缝扩展的数值模拟研究[博士学位论文][D]. 合肥:中国科学技术大学,2011.(BIAO Fangjun. Numerical simulation of horizontal fracture propagation in hydraulic fracturing[Ph. D. Thesis][D]. Hefei:University of Science and Technology of China,2011.(in Chinese))
[5] 程 万. 三维空间下裂缝性页岩储层水力裂缝扩展机制研究[博士学位论文][D]. 北京:中国石油大学,2016.(CHENG Wan. Research on hydraulic fracture propagation mechanism of fractured shale reservoir in three-dimensional space[Ph. D. Thesis][D]. Beijing:China University of Petroleum,2016.(in Chinese))
[6] 李正军. 基于最小耗能原理水力压裂裂缝启裂及扩展规律研究[博士学位论文][D]. 大庆:东北石油大学,2011.(LI Zhengjun. Research on the law of fracture initiation and propagation of hydraulic fracturing based on the principle of minimum energy consumption[Ph. D. Thesis][D]. Daqing:Northeast Petroleum University,2011.(in Chinese))
[7] XIE J,TANG J,YONG R,et al. A 3-D hydraulic fracture propagation model applied for shale gas reservoirs with multiple bedding planes[J]. Engineering Fracture Mechanics,2020,228:106872.
[8] CHONG K P,KURUPPU M D. New specimen for fracture toughness determination of rock and other materials[J]. International Journal of Fracture,1984,26(2):R59–R62.
[9] CHONG K P,KURUPPU M D,KUSZMAUL J S. Fracture toughness determination of layered materials[J]. Engineering Fracture Mechanics,1987,28(1):43–54.
[10] KATAOKA M,OBARA Y,KURUPPU M. Estimation of fracture toughness of anisotropic rocks by semi-circular bend(SCB) tests under water vapor pressure[J]. Rock Mechanics and Rock Engineering,2015,48(4):1 353–1 367.
[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] LEE H P,OLSON J E,SCHULTZ R A. Interaction analysis of propagating opening mode fractures with veins using the discrete element method[J]. International Journal of Rock Mechanics and Mining Sciences,2018,103:275–288.
[13] CHANDLER M R,MEREDITH P G,BRANTUT N,et al. Fracture toughness anisotropy in shale[J]. Journal of Geophysical Research Solid Earth,2016,121:1 706–1 729.
[14] NA S H,SUN W C,INGRAHAM M D,et al. Effects of spatial heterogeneity and material anisotropy on the fracture pattern and macroscopic effective toughness of mancos shale in brazilian tests[J]. Journal of Geophysical Research Solid Earth,2017,122(8):6 202– 6 230.
[15] SHANG J,GUI Y,ZHAO Z. Broad-spectrum fracture toughness of an anisotropic sandstone under mixed-mode loading[J]. Theoretical and Applied Fracture Mechanics,2018,96:556–575.
[16] 赵子江,刘大安,崔振东,等. 半圆盘三点弯曲法测定页岩断裂韧度(K_(IC))的实验研究[J]. 岩土力学,2018,39(增1):267–275. (ZHAO Zijiang,LIU Da¢an,CUI Zhendong,et al. Experimental study on the determination of shale fracture toughness(K_(IC)) by the three-point bending method of semi-disc[J]. Rock and Soil Mechanics,2018,39(Supp.1):267–275.(in Chinese))
[17] 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. Experimental study on the influence of bedding direction on sandstone fracture mode and toughness[J]. Chinese Journal of Geotechnical Engineering,2019,41(10):1 854–1 862.(in Chinese))
[18] 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):138–148.(LI Bin,HUANG Da,MA Wenzhu. Study on the influence of bedding surface characteristics on the fracture mechanical behavior of sandstone[J]. Rock and Soil Mechanics,2020,41(3):138–148.(in Chinese))
[19] SAGHAFI H,AYATOLLAHI M R,SISTANINIA M. A modified MTS criterion(MMTS) for mixed-mode fracture toughness assessment of brittle materials[J]. Materials Science and Engineering:A(Structural Materials:Properties,Microstructure and Processing),2010,527(21/22):5 624–5 630.
[20] DARBAN H,HAGHPANAHI M,ASSADI A. Determination of crack tip parameters for ASCB specimen under mixed mode loading using finite element method[J]. Computational Materials Science,2011,50(5):1 667–1 674.
[21] AYATOLLAHI M R,ALIHA M R M,SAGHAFI H. An improved semi-circular bend specimen for investigating mixed mode brittle fracture[J]. Engineering Fracture Mechanics,2011,78(1):110–123.
[22] MARSAVINA L,CONSTANTINESCU D M,LINUL E,et al. Refinements on fracture toughness of PUR foams[J]. Engineering Fracture Mechanics,2014,129:54–66.
[23] NEJATI M,AMINZADEH,SAAR M O,et al. Modified semi-circular bend test to determine the fracture toughness of anisotropic rocks[J]. Engineering Fracture Mechanics,2019,213:153–171.
[24] 赵毅鑫,孙 荘,刘 斌. 忻州窑烟煤I型和II型断裂特性的半圆弯曲试验对比研究[J]. 岩石力学与工程学报,2019,38(8):1 593– 1 604.(ZHAO Yixin,SUN Zong,LIU Bin. Comparative study on the fracture characteristics of Xinzhouyao bituminous coal with type I and type II in semicircular bending test[J]. Chinese Journal of Rock Mechanics and Engineering,2019,38(8):1 593–1 604.(in Chinese))
[25] Itasca Consulting Group Inc.. PFC version 5.0[R]. Minneapolis:Itasca Consulting Group Inc.,2014.
[26] 卞 康,陈彦安,刘 建,等. 不同吸水时间下页岩卸荷破坏特征的颗粒离散元研究[J]. 岩土力学,2020,41(增1):355–367.(BIAN Kang,CHEN Yan¢an,LIU Jian,et al. Study on unloading failure characteristics of shale under different water absorption time by particle discrete element method[J]. Rock and Soil Mechanics,2020,41(Supp.1):355–367.(in Chinese))
[27] CAO R H,CAO P,FAN X,et al. An experimental and numerical study on mechanical behavior of ubiquitous-joint brittle rock-like specimens under uniaxial compression[J]. Rock Mechanics and Rock Engineering,2016,49(11):1–20.
[28] 陈彦安,崔德山,卞 康,等. 含共面双裂隙复合岩样力学特征的颗粒流分析[J]. 安全与环境工程,2020,27(2):140–148.(CHEN Yan¢an,CUI Deshan,BIAN Kang,et al. Particle flow analysis of mechanical characteristics of a composite rock sample with coplanar double fractures[J]. Safety and Environmental Engineering,2020,27(2):140–148.(in Chinese))
[29] 范 祥,曹 平. 基于 PFC3D 单轴压缩下含2 条裂隙试样力学行为的数值分析[J]. 中南大学学报:自然科学版,2015,46(7):2 635–2 642.(FAN Xiang,CAO Ping. Numerical analysis of mechanical behavior of a specimen with two cracks under uniaxial compression based on PFC3D[J]. Journal of Central South University:Natural Science,2015,46(7):2 635–2 642.(in Chinese))
[30] LUC S,DONZÉ F V. Modelling progressive failure in fractured rock masses using a 3D discrete element method[J]. International Journal o f Rock Mechanics and Mining Sciences,2012,52(6):18–30.
[31] ZHANG C H,PEKAU O A, FENG J,et al. Application of distinct element method in dynamic analysis of high rock slopes and blocky structures[J]. Soil Dynamics and Earthquake Engineering,1997,16(6):385–394.
[32] 岑夺丰,黄 达,黄润秋. 块裂反倾巨厚层状岩质边坡变形破坏颗粒流模拟及稳定性分析[J]. 中南大学学报:自然科学版,2016,47(3):984–993.(CEN Duofeng,HUANG Da,HUANG Runqiu. Granular flow simulation and stability analysis of deformation and failure of block-cracked anti-dipping huge-thick layered rock slope[J]. Journal of Central South University:Natural Science,2016,47(3):984–993.(in Chinese))
[33] ROY D G,SINGH T N,KODIKARA J. Influence of joint anisotropy on the fracturing behavior of a sedimentary rock[J]. Engineering Geology,2017:228(13):224–237.
[34] 韩振华,张路青,周 剑. 基于PFC2D模拟的矿物粒径非均质效应研究[J]. 工程地质学报,2019,27(4):706–716.(HAN Zhenhua,ZHANG Luqing,ZHOU Jian. Research on the heterogeneous effect of mineral particle size based on PFC2D simulation[J]. Journal of Engineering Geology,2019,27(4):706–716.(in Chinese))
[35] SHANG J,HENCHER S R,WEST L J. Tensile strength of geological discontinuities including incipient bedding,rock joints and mineral veins[J]. Rock Mechanics and Rock Engineering,2016:49:4 213– 4 224.
[36] SHANG J,DUAN K,GUI Y,et al. Numerical investigation of the direct tensile behaviour of laminated and transversely isotropic rocks containing incipient bedding planes with different strengths[J]. Computers and Geotechnics,2018,104(DEC):373–388.
[37] FAKHIMI A,VILLEGAS T. Application of dimensional analysis in calibration of a discrete element model for rock deformation and fracture[J]. Rock Mechanics and Rock Engineering,2007,40(2):193–211.
[38] YOON J. Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation[J]. International Journal of Rock Mechanics and Mining Sciences,2007,44(6):871–889.
[39] WENG M C,LI H H,Relationship between the deformation characteristics and microscopic properties of sandstone explored by the bonded-particle model[J]. International Journal of Rock Mechanics and Mining Sciences,2012,56:34–43.
[40] ZHANG X P,WONG L N Y.Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression[J]. International Journal of Fracture,2013,180(1):93–110.
[41] FUNATSU T,SHIMIZU N,KURUPPU M,et al. Evaluation of mode I fracture toughness assisted by the numerical determination of K-Resistance[J]. Rock Mechanics and Rock Engineering,2015,48(1):143–157.
[42] IRWIN G R. Analysis of stresses and strains near the end of a crack traversing a plate[J]. Journal of Applied Mechanics-Transactions of the ASME,1957,24:351–369.
[43] RICE J R. A path independent integral and approximate analysis of strain concentration by notches and cracks[J]. Journal of Applied Mechanics,1968,35:379–386.
[44] 李世愚,岩石断裂力学导论[M]. 合肥:中国科学技术大学出版社,2009:89–98.(LI Shiyu,Introduction to rock fracture mechanics[M]. Hefei:University of Science and Technology of China Press,2009:89–98.(in Chinese)) |
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