试验设计法在硬岩PFC~(3D)模型细观参数标定中的应用
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摘要
利用试验设计法针对硬质岩体颗粒离散元数值研究中的细观参数标定问题进行了研究。首先利用Plackett-Burman试验设计分析了细观参数对宏观响应的敏感性,并建立了宏观力学指标和细观参数之间的线性关系,然后利用响应曲面法考查了显著影响参数之间的相互作用,得到了宏观响应与细观参数之间的非线性关系。最后将问题转化为非线性多目标数学规划问题利用MATLAB软件中FGOALATTAIN函数进行求解。通过和典型硬岩物理试验结果对比发现,利用试验设计法标定参数建立的颗粒离散元模型可以很好地反映单轴和低围压下岩石的破坏过程,但是由于采用了球形颗粒对于高围压下的拟合效果偏弱。利用PB设计、响应曲面法并结合数学规划建立的细观参数标定方法可以反映各细观参数对宏观力学响应的敏感性并给出明确的函数表达式,同时可以通过增加求解过程中的约束条件来体现更多的岩石力学特性。
The design of experiments(DOE) is used to study the microscopic parameter calibration for hard rocks of PFC~(3D) model. Firstly, the sensitivity of microscopic parameters to macroscopic responses is analyzed through the Plackett-Burman design. The linear relationship between microscopic parameters and macroscopic responses is established. Then, the interaction between microscopic parameters is investigated by using the response surface method(RSM) and the nonlinear relationship between microscopic parameters and macroscopic responses is obtained. Finally, the problem is transformed into a nonlinear multiobjective mathematical programming problem, and the FGOALATTAIN function in MATLAB software is utilized to solve the problem. It can be found that when using DOE to calibrate the microscopic parameters, the PFC~(3D) model can well reflect the failure process of the rock under uniaxial and low confining compression conditions. However, the fitting results under high confining pressure is unsatisfactory. The method based on the PB design, response surface method and mathematical programming can reflect the sensitivity of the microscopic parameters, and the definite function expressions are obtained. At the same time, it can reflect more characteristics of rock mechanics by adding the constraints condition in the process of solving.
The design of experiments(DOE) is used to study the microscopic parameter calibration for hard rocks of PFC~(3D) model. Firstly, the sensitivity of microscopic parameters to macroscopic responses is analyzed through the Plackett-Burman design. The linear relationship between microscopic parameters and macroscopic responses is established. Then, the interaction between microscopic parameters is investigated by using the response surface method(RSM) and the nonlinear relationship between microscopic parameters and macroscopic responses is obtained. Finally, the problem is transformed into a nonlinear multiobjective mathematical programming problem, and the FGOALATTAIN function in MATLAB software is utilized to solve the problem. It can be found that when using DOE to calibrate the microscopic parameters, the PFC~(3D) model can well reflect the failure process of the rock under uniaxial and low confining compression conditions. However, the fitting results under high confining pressure is unsatisfactory. The method based on the PB design, response surface method and mathematical programming can reflect the sensitivity of the microscopic parameters, and the definite function expressions are obtained. At the same time, it can reflect more characteristics of rock mechanics by adding the constraints condition in the process of solving.
引文
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[11]WANG Y,TONON F.Calibration of a discrete element model for intact rock up to its peak strength[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(5):447-469.
[12]王永菲,王成国.响应面法的理论与应用[J].中央民族大学学报:自然科学版,2005,14(3):236-240.(WANGYong-fei,WANG Cheng-guo.The application of response surface methodology[J].Journal of The Central University For Nationalities(Natural Science Edition),2005,14(3):236-240.(in Chinese))
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[17]EBERHARDT E,STEAD D,STIMPSON B.Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(3):361-380.
[18]EBERHARDT E.Brittle rock fracture and progressive damage in uniaxial compression[D].Saskatoon:University of Saskatchewan,1998.
[19]YOON K.Deformation and fracturing of rock by acoustic emission measurement and bonded-particle model analysis[D].Seoul:School of Civil,Urban and Geosystem Engineering,Seoul National University,2002.
[20]PLACKETT R L,BURMAN J P.The design of optimum multifactorial experiments[J].Biometrika,1946,33(4):305-325.
[21]VAN MIER J G.Microstructural effects on fracture scaling in concrete,rock and ice[C]//IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics.Springer,2001.
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[23]VAN VLIET M R A.Size effect in tensile fracture of concrete and rock[M].Delft:Delft University of Technology,2000.
[24]刘振学,黄仁和,田爱民.实验设计与数据处理[M].北京:化学工业出版社,2005.(LIU Zhen-xue,HUANG Ren-he,TIAN Ai-min.Experimental design and data processing[M].Beijing:Chemical Industry Press,2005.(in Chinese))
[25]徐向宏,何明珠.试验设计与Design-Expert,SPSS应用[M].北京:科学出版社,2010.(XU Xiang-hong,HEMing-zhu.Experimental design and design-expert,SPSSapplication[M].Beijing:Science Press,2010.(in Chinese))
[26]傅珏生,张健,王振羽,等.实验设计与分析[M].北京:人民邮电出版社,2009.(FU Yu-sheng,ZHANG Jian,WANG Zhen-yu,et al.Experimental design and analysis[M].Beijing:People's Posts and Telecommunications Press,2009.(in Chinese))
[27]AL-SHAYEA N,KHAN K,ABDULJAUWAD S.Effects of confining pressure and temperature on mixed-mode(I-II)fracture toughness of a limestone rock[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(4):629-643.
[28]RAO Q,SUN Z,STEPHANSSON O,et al.Shear fracture(Mode II)of brittle rock[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(3):355-375.
[29]BACKERS T.Fracture toughness determination and micromechanics of rock under mode I and mode IIloading[D].Potsdam:Universit?t Potsdam,2005.
[30]陈亮,刘建锋,王春萍,等.北山深部花岗岩弹塑性损伤模型研究[J].岩石力学与工程学报,2013,32(2):289-298.(CHEN Liang,LIU Jian-feng,WANG Chun-ping.Elastoplastic damage model of Beishan deep granite[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(2):289-298.(in Chinese))
[31]杨圣奇,苏承东,徐卫亚.大理岩常规三轴压缩下强度和变形特性的试验研究[J].岩土力学,2005,26(3):475-478.(YANG Sheng-qi,SU Cheng-dong,XU Wei-ya.Experimental investigation on strength and deformation properties of marble under conventional triaxial compression[J].Rock Soil Mechanics,2005,26(3):475-478.(in Chinese))
[2]尹小涛,李春光,王水林,等.岩土材料细观、宏观强度参数的关系研究[J].固体力学学报,2011,32(增刊1):343-351.(YIN Xiao-tao,LI Chun-guang,WANG Shui-lin,et al.Study on relationship between micro-parameters and macroparameters of rock and soil material[J].Chinese Journal of Solid Mechanics,2011,32(S1):343-351.(in Chinese))
[3]刘新荣,傅晏,郑颖人,等.颗粒流细观强度参数与岩石断裂韧度之间的关系[J].岩石力学与工程学报,2011,30(10):2084-2089.(LIU Xin-rong,FU Yan,ZHENGYing-ren,et al.Relation between meso-parameters of particle flow code and fracture toughness of rock[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(10):2084-2089.(in Chinese))
[4]周博,汪华斌,赵文锋,等.黏性材料细观与宏观力学参数相关性研究[J].岩土力学,2012,33(10):3171-3175+3177-3178.(ZHOU Bo,WANG Hua-bin,ZHAOWen-feng,et al.Analysis of relationship between particle mesoscopic and macroscopic mechanical parameters of cohesive materials[J].Rock Soil Mechanics,2012,33(10):3171-3178.(in Chinese))
[5]赵国彦,戴兵,马驰.平行黏结模型中细观参数对宏观特性影响研究[J].岩石力学与工程学报,2012,31(7):1491-1498.(ZHAO Guo-yan,DAI Bing,MA Chi.Study of effects of microparameters on macroproperties for parallel bonded model[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(7):1491-1498.(in Chinese))
[6]丛宇,王在泉,郑颖人,等.基于颗粒流原理的岩石类材料细观参数的试验研究[J].岩土工程学报,2015,37(6):1031-1040.(CONG Yu,WANG Zai-quan,ZHENGYing-ren,et al.Experimental study on microscopic parameters of brittle materials based on particle flow theory[J].Chinese Journal of Geotechnical Engineering,2015,37(6):1031-1040.(in Chinese))
[7]POTYONDY D O,CUNDALL P A.A bonded-particle model for rock[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1329-1364.
[8]YOON J,STEPHANSSON O,DRESEN G.Application of design of experiments to process improvement of PFC model calibration in uniaxial compression simulation[C]//Proceedings of the 4th Asian Rock Mechanics Symposium(ARMS-4).Singapore,2004.
[9]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.
[10]COETZEE C J,ELS D N J.Calibration of discrete element parameters and the modelling of silo discharge and bucket filling[J].Computers and Electronics in Agriculture,2009,65(2):198-212.
[11]WANG Y,TONON F.Calibration of a discrete element model for intact rock up to its peak strength[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(5):447-469.
[12]王永菲,王成国.响应面法的理论与应用[J].中央民族大学学报:自然科学版,2005,14(3):236-240.(WANGYong-fei,WANG Cheng-guo.The application of response surface methodology[J].Journal of The Central University For Nationalities(Natural Science Edition),2005,14(3):236-240.(in Chinese))
[13]CHEN X,MIEDEMA S A,RHEE C V.Application of parallel bond method in rock compression simulation[C]//Proceedings of the 5th International Dredging Technology Development Conference of China.Tianjin,2017.
[14]PFC3D U M.Itasca consulting group[M].Minneapolis:Inc,2005.
[15]尤明庆.岩石试样的强度及变形破坏过程[M].北京:地质出版社,2000.(YOU Ming-qing.The strength and deformation process of rock specimen[M].Beijing:Geological Publishing House,2000.(in Chinese))
[16]POTYONDY D O,CUNDALL P A.A bonded-particle model for rock[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1329-1364.
[17]EBERHARDT E,STEAD D,STIMPSON B.Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression[J].International Journal of Rock Mechanics and Mining Sciences,1999,36(3):361-380.
[18]EBERHARDT E.Brittle rock fracture and progressive damage in uniaxial compression[D].Saskatoon:University of Saskatchewan,1998.
[19]YOON K.Deformation and fracturing of rock by acoustic emission measurement and bonded-particle model analysis[D].Seoul:School of Civil,Urban and Geosystem Engineering,Seoul National University,2002.
[20]PLACKETT R L,BURMAN J P.The design of optimum multifactorial experiments[J].Biometrika,1946,33(4):305-325.
[21]VAN MIER J G.Microstructural effects on fracture scaling in concrete,rock and ice[C]//IUTAM Symposium on Scaling Laws in Ice Mechanics and Ice Dynamics.Springer,2001.
[22]VAN MIER J G.Fracture processes of concrete[M].Florida:CRC Press,1996.
[23]VAN VLIET M R A.Size effect in tensile fracture of concrete and rock[M].Delft:Delft University of Technology,2000.
[24]刘振学,黄仁和,田爱民.实验设计与数据处理[M].北京:化学工业出版社,2005.(LIU Zhen-xue,HUANG Ren-he,TIAN Ai-min.Experimental design and data processing[M].Beijing:Chemical Industry Press,2005.(in Chinese))
[25]徐向宏,何明珠.试验设计与Design-Expert,SPSS应用[M].北京:科学出版社,2010.(XU Xiang-hong,HEMing-zhu.Experimental design and design-expert,SPSSapplication[M].Beijing:Science Press,2010.(in Chinese))
[26]傅珏生,张健,王振羽,等.实验设计与分析[M].北京:人民邮电出版社,2009.(FU Yu-sheng,ZHANG Jian,WANG Zhen-yu,et al.Experimental design and analysis[M].Beijing:People's Posts and Telecommunications Press,2009.(in Chinese))
[27]AL-SHAYEA N,KHAN K,ABDULJAUWAD S.Effects of confining pressure and temperature on mixed-mode(I-II)fracture toughness of a limestone rock[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(4):629-643.
[28]RAO Q,SUN Z,STEPHANSSON O,et al.Shear fracture(Mode II)of brittle rock[J].International Journal of Rock Mechanics and Mining Sciences,2003,40(3):355-375.
[29]BACKERS T.Fracture toughness determination and micromechanics of rock under mode I and mode IIloading[D].Potsdam:Universit?t Potsdam,2005.
[30]陈亮,刘建锋,王春萍,等.北山深部花岗岩弹塑性损伤模型研究[J].岩石力学与工程学报,2013,32(2):289-298.(CHEN Liang,LIU Jian-feng,WANG Chun-ping.Elastoplastic damage model of Beishan deep granite[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(2):289-298.(in Chinese))
[31]杨圣奇,苏承东,徐卫亚.大理岩常规三轴压缩下强度和变形特性的试验研究[J].岩土力学,2005,26(3):475-478.(YANG Sheng-qi,SU Cheng-dong,XU Wei-ya.Experimental investigation on strength and deformation properties of marble under conventional triaxial compression[J].Rock Soil Mechanics,2005,26(3):475-478.(in Chinese))