基于统计试验设计下花岗岩两种本构模型研究
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摘要
针对颗粒离散元在研究岩石材料过程中细观本构模型表现出的差异性问题,以新疆奇热哈塔尔过水隧洞片麻状花岗岩的力学参数为基础,建立二维离散元模型,通过统计学的试验方法,对比分析PB模型与FJ模型在宏观力学参数及破坏模式的差异性与稳定性,为后续改进本构模型以及选取合适的本构模型进行岩石数值模拟提供研究依据。研究表明,两种本构模型均能做到较为准确描述花岗岩的宏观力学参数,从计算稳定性角度来讲,PB模型计算结果更具有确定性,但表征不出准确压拉比;从统计学分析结果以及破坏模式来看,利用PB模型研究均质性较强且抗拉强度较高的硬岩材料的力学行为时具有一定优势;而对于均质性较弱且压拉比较高的硬岩材料,FJ模型由于其破坏模式的不确定性更能表现出岩石材料的非均质性。结果说明,PB与FJ两种本构模型各有优劣,今后在进行花岗岩等硬性岩石数值试验时,可根据岩石特性以及研究内容,选择合适的本构模型。
In view of the differences for the discrete particle in the meso-constitutive model in process of studying rock materials,heatwaves in xinjiang ha thar mechanical parameters of a water tunnel gneissic granite,on the basis of two-dimensional discrete element model is established,through statistical test methods,the differences and stability of macroscopic mechanical parameters and failure modes between the PB model and the FJ model are compared and analyzed,the research basis is provided for the subsequent improvement of the constitutive model and the selection of a suitable constitutive model for rock numerical simulation. The results show that although both constitutive models can describe the macroscopic mechanical parameters of rock materials accurately,the calculation results of the PB model are more deterministic than those of the PB model,but they cannot be characterized accurately; from the results of statistical analysis and the failure mode,the PB model has certain advantages in the study of the mechanical behavior of hard rock materials with high homogeneity and high tensile strength,whereas hard rock materials with relatively low homogeneity and relatively high pressure pulls have certain advantages,the FJ model can show the heterogeneity of rock materials because of the uncertainty of its failure mode. The results show that two constitutive models of PB and FJ have their advantages and disadvantages,the appropriate constitutive model can be selected based on the rock properties in the future and the research content when performing the numerical tests on hard rocks.
In view of the differences for the discrete particle in the meso-constitutive model in process of studying rock materials,heatwaves in xinjiang ha thar mechanical parameters of a water tunnel gneissic granite,on the basis of two-dimensional discrete element model is established,through statistical test methods,the differences and stability of macroscopic mechanical parameters and failure modes between the PB model and the FJ model are compared and analyzed,the research basis is provided for the subsequent improvement of the constitutive model and the selection of a suitable constitutive model for rock numerical simulation. The results show that although both constitutive models can describe the macroscopic mechanical parameters of rock materials accurately,the calculation results of the PB model are more deterministic than those of the PB model,but they cannot be characterized accurately; from the results of statistical analysis and the failure mode,the PB model has certain advantages in the study of the mechanical behavior of hard rock materials with high homogeneity and high tensile strength,whereas hard rock materials with relatively low homogeneity and relatively high pressure pulls have certain advantages,the FJ model can show the heterogeneity of rock materials because of the uncertainty of its failure mode. The results show that two constitutive models of PB and FJ have their advantages and disadvantages,the appropriate constitutive model can be selected based on the rock properties in the future and the research content when performing the numerical tests on hard rocks.
引文
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[14]蔡美峰.岩石力学与工程[M]．第2版.北京:科学出版社，2013.
[15]孙其诚，程晓辉，季顺迎，等.岩土类颗粒物质宏-细观力学研究进展[J]．力学进展，2011(3):351-371.
[16]尹小涛，郑亚娜，马双科.基于颗粒流数值试验的岩土材料内尺度比研究[J]．岩土力学，2011,32(4):1211-1215.
[17]伍文龙，袁林娟，张锐，等.基于统计损伤理论的邓肯-张修正模型研究[J]．水利水电技术，2017,48(4):131-135.
[2] POTYONDY D O. The Bonded-particle Model as a Tool for Rock Mechanics Research and Application:Current Trends and Future Directions[J]. Geosystem Engineering,2015,18(1):1-28.
[3]蒋明镜，陈贺，刘芳.岩石微观胶结模型及离散元数值仿真方法初探[J]．岩石力学与工程学报，2013,32(1):15-23.
[4] POTYONDY D O. A Flat-Jointed Bonded-Particle Material for Hard Rock[Z]. American Rock Mechanics Association,2012.
[5]刘富有，陈鹏宇.基于Flatjoint接触模型的岩石单轴压缩和巴西劈裂颗粒流模拟研究[J]．长江科学院院报，2016,33(9):60-65.
[6]陈鹏宇，余宏明.平直节理黏结颗粒材料宏细观参数关系及细观参数的标定[J]．土木建筑与环境工程，2016,38(5):74-84.
[7] JOHNSON R A,BHATTACHARYYA G K. Statistics:Principles and Methods[M]. Hoboken:John Wiley﹠Sons,2009.
[8] GB 4882-1985，数据的统计处理和解释正态性检验[S].
[9] RICE J. Mathematical Statistics and Data Analysis[M]. International Edition(with CD Data Sets),Wadsworth,2006.
[10] GASTWIRTH J L,GEL Y R,MIAO W. The Impact of Levene's Test of Equality of Variances on Statistical Theory and Practice[J]. Statistical Science,2010,24(3):343-360.
[11] ELLIOTT A C,HYNAN L S. A SAS Macro Implementation of a Multiple Comparison Post hoc Test for a Kruskal-Wallis Analysis[J]. Computer Methods&Programs in Biomedicine,2011,102(1):75-80.
[12]宿辉，党承华，李彦军.考虑不均质度的岩石声发射数值模拟研究[J]．岩土力学，2011,32(6):1886-1890.
[13] WU SHUNCHUAN,XU XUELIANG. A Study of Three Intrinsic Problems of the Classic Discrete Element Method Using Flat-Joint Model[J]. Rock Mechanics Rock Engineering,2016(49):1813-1830.
[14]蔡美峰.岩石力学与工程[M]．第2版.北京:科学出版社，2013.
[15]孙其诚，程晓辉，季顺迎，等.岩土类颗粒物质宏-细观力学研究进展[J]．力学进展，2011(3):351-371.
[16]尹小涛，郑亚娜，马双科.基于颗粒流数值试验的岩土材料内尺度比研究[J]．岩土力学，2011,32(4):1211-1215.
[17]伍文龙，袁林娟，张锐，等.基于统计损伤理论的邓肯-张修正模型研究[J]．水利水电技术，2017,48(4):131-135.