粗粒土三维细观组构与本构关系研究
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摘要
运用数学统计方法研究具有方向和大小的粗粒土组构、接触力、枝矢量等与粗粒土本构之间的多尺度关系。通过统计概率的方法进行分析含有一定项数单位向量的多项式接触方向概率分布密度函数(组构张量)和矩张量;运用最小二乘法来确定组构张量展开成3种不同形式多项式表达式系数,建立3种形式组构张量与已知数据统计表达式之间的联系,通过正交分解使展开式各项相互独立,构建粗粒土细观参数组构、接触力、枝矢量与粗粒土应力的表达式。对比钢珠三轴试验和数值计算的宏细观应力,二者结果基本一致,且二阶颗粒接触法向接触密度分布函数能较好描述颗粒接触组构。研究得到的粗粒土细观参数应力表达式为三维条件下粗粒土应力–接触力–组构数值模拟奠定理论基础。
Coarse aggregate multi-scale study is mainly to establish the connection between fabric,contact forces,branch vector and constitutive relation,through probability statistics method for the direction and magnitude of the coarse aggregate orientational tensor. It gets a certain number of unit vector directional of contact probability distribution density function(fabric) and moment tensor by the method of statistical probability. The fabric tensor spread out three different forms polynomial expressions using least-square method to determine correlation coefficients. Three types of fabric tensor and the known data expression of statistics the relationship are set up. Orthogonal decomposition is used to make expansion independent with each other. Coarse aggregate stress expressions which included microstructure parameters fabric,contact force and branch vector are built. Compared with steel balls triaxial test and numerical calculation contrast macro-mesoscopic stress,two results are consistent. The simulation results indicate that second-rank contact normal density distribution function give reasonable approximations. A theoretical basis has been established for numerical simulation and the stress expressions for coarse aggregate microscopic parameters under the condition of three dimensional stress-contact force-fabrics.
Coarse aggregate multi-scale study is mainly to establish the connection between fabric,contact forces,branch vector and constitutive relation,through probability statistics method for the direction and magnitude of the coarse aggregate orientational tensor. It gets a certain number of unit vector directional of contact probability distribution density function(fabric) and moment tensor by the method of statistical probability. The fabric tensor spread out three different forms polynomial expressions using least-square method to determine correlation coefficients. Three types of fabric tensor and the known data expression of statistics the relationship are set up. Orthogonal decomposition is used to make expansion independent with each other. Coarse aggregate stress expressions which included microstructure parameters fabric,contact force and branch vector are built. Compared with steel balls triaxial test and numerical calculation contrast macro-mesoscopic stress,two results are consistent. The simulation results indicate that second-rank contact normal density distribution function give reasonable approximations. A theoretical basis has been established for numerical simulation and the stress expressions for coarse aggregate microscopic parameters under the condition of three dimensional stress-contact force-fabrics.
引文
[1]齐吉琳,谢定义,石玉成.土结构性的研究方法及现状[J].西北地震学报,2001,23(1):99–103.(QI Jilin,XIE Dingyi,SHI Yucheng.Status quo and method of quantitative on soil structure[J].Northwestern Seismological Journal,2001,23(1):99–103.(in Chinese))
[2]钟晓雄,袁建新.颗粒材料的剪胀模型[J].岩土力学,1992,13(1):1–10.(ZHONG Xiaoxiong,YUAN Jianxin.Shear dilating model of granular materials[J].Rock and Soil Mechanics,1992,13(1):1–10.(in Chinese))
[3]姜景山,程展林,刘汉龙,等.粗粒土二维模型试验的组构分析[J].岩土工程学报,2009,31(5):811–816.(JIANG Jingshan,CHENG Zhanlin,LIU Hanlong,et al.Fabric analysis of two-dimensional tests for coarse-grained soils[J].Chinese Journal of Geotechnical Engineering,2009,31(5):811–816.(in Chinese))
[4]吴良平.粗粒土组构试验研究[硕士学位论文][D].武汉:长江科学院,2007.(WU Liangping.Study on the microfabric of coarse aggregate[M.S.Thesis][D].Wuhan:Yangtze River Scientific Research Institute,2007.(in Chinese))
[5]史旦达,周健,刘白文,等.砂土直剪力学性状的非圆颗粒模拟与宏细观机理研究[J].岩土工程学报,2010,32(10):1 157–1 565.(SHI Danda,ZHOU Jian,LIU Baiwen,et al.Exploring macro-and micro-scale responses of sand in direct shear tests by numerical simulations using non-circular particles[J].Chinese Journal of Geotechnical Engineering,2010,32(10):1 157–1 565.(in Chinese))
[6]KANATANI K.Distribution of directional data and fabric tensors[J].International Journal of Engineering Science,1984,22(2):149–164.
[7]ROTHENBURG L,BATHURST R J.Analytical study of induced anisotropy in idealized granular materials[J].Geotechnique,1989,39(4):601–614.
[8]ROTHENBURG L,KRUYT N P.Micromechanical definition of an entropy for quasi-static deformation of granular materials[J].Journal of the Mechanics and Physics of Solids,2009,57(3):634–655.
[9]JANG E R,JUNG Y H,CHUNG C K.Stress ratio–fabric relationships of granular soils under axisymmetric stress and plane-strain loading[J].Computers and Geotechnics,2010,37(7/8):913–929.
[10]LI X,YU H S.Applicability of stress-force-fabric relationship for non-proportional loading[J].Computers and Structures,2011,89(11/12):1 094–1 102.
[11]NICOT F,DARVE F,GROUP R,et al.A multi-scale approach to granular materials[J].Mechanics of Materials,2005,37(9):980–1 006.
[12]VARGA P,ZYSSET P K.Sampling sphere orientation distribution:An efficient method to quantify trabecular bone fabric on grayscale images[J].Medical Image Analysis,2009,13:530–541.
[13]MILLET O,GU S T,KONDO D.A 4th order fabric tensor approach applied to granular media[J].Computers and Geotechnics,2009,36(5):736–742.
[14]YANG Q,CHEN X,ZHOU W Y.Effective stress and vector-valued orientational distribution functions[J].International Journal of Damage Mechanics,2008,17:101–121.
[15]BAGI K.Microstructural stress tensor of granular assemblies with volume forces[J].Journal of Applied Mechanics,1999,66(4):934–936.
[16]JANG E R,JUNG Y H,CHUNG C K.Stress ratio–fabric relationships of granular soils under axisymmetric stress and plane-strain loading[J].Computers and Geotechnics,2010,37(7/8):913–929.
[2]钟晓雄,袁建新.颗粒材料的剪胀模型[J].岩土力学,1992,13(1):1–10.(ZHONG Xiaoxiong,YUAN Jianxin.Shear dilating model of granular materials[J].Rock and Soil Mechanics,1992,13(1):1–10.(in Chinese))
[3]姜景山,程展林,刘汉龙,等.粗粒土二维模型试验的组构分析[J].岩土工程学报,2009,31(5):811–816.(JIANG Jingshan,CHENG Zhanlin,LIU Hanlong,et al.Fabric analysis of two-dimensional tests for coarse-grained soils[J].Chinese Journal of Geotechnical Engineering,2009,31(5):811–816.(in Chinese))
[4]吴良平.粗粒土组构试验研究[硕士学位论文][D].武汉:长江科学院,2007.(WU Liangping.Study on the microfabric of coarse aggregate[M.S.Thesis][D].Wuhan:Yangtze River Scientific Research Institute,2007.(in Chinese))
[5]史旦达,周健,刘白文,等.砂土直剪力学性状的非圆颗粒模拟与宏细观机理研究[J].岩土工程学报,2010,32(10):1 157–1 565.(SHI Danda,ZHOU Jian,LIU Baiwen,et al.Exploring macro-and micro-scale responses of sand in direct shear tests by numerical simulations using non-circular particles[J].Chinese Journal of Geotechnical Engineering,2010,32(10):1 157–1 565.(in Chinese))
[6]KANATANI K.Distribution of directional data and fabric tensors[J].International Journal of Engineering Science,1984,22(2):149–164.
[7]ROTHENBURG L,BATHURST R J.Analytical study of induced anisotropy in idealized granular materials[J].Geotechnique,1989,39(4):601–614.
[8]ROTHENBURG L,KRUYT N P.Micromechanical definition of an entropy for quasi-static deformation of granular materials[J].Journal of the Mechanics and Physics of Solids,2009,57(3):634–655.
[9]JANG E R,JUNG Y H,CHUNG C K.Stress ratio–fabric relationships of granular soils under axisymmetric stress and plane-strain loading[J].Computers and Geotechnics,2010,37(7/8):913–929.
[10]LI X,YU H S.Applicability of stress-force-fabric relationship for non-proportional loading[J].Computers and Structures,2011,89(11/12):1 094–1 102.
[11]NICOT F,DARVE F,GROUP R,et al.A multi-scale approach to granular materials[J].Mechanics of Materials,2005,37(9):980–1 006.
[12]VARGA P,ZYSSET P K.Sampling sphere orientation distribution:An efficient method to quantify trabecular bone fabric on grayscale images[J].Medical Image Analysis,2009,13:530–541.
[13]MILLET O,GU S T,KONDO D.A 4th order fabric tensor approach applied to granular media[J].Computers and Geotechnics,2009,36(5):736–742.
[14]YANG Q,CHEN X,ZHOU W Y.Effective stress and vector-valued orientational distribution functions[J].International Journal of Damage Mechanics,2008,17:101–121.
[15]BAGI K.Microstructural stress tensor of granular assemblies with volume forces[J].Journal of Applied Mechanics,1999,66(4):934–936.
[16]JANG E R,JUNG Y H,CHUNG C K.Stress ratio–fabric relationships of granular soils under axisymmetric stress and plane-strain loading[J].Computers and Geotechnics,2010,37(7/8):913–929.
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