基于细观层次混凝土静、动力学性能的数值模拟
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摘要
本文从细观层次入手,把混凝土看作是由骨料、界面和砂浆组成的非均质复合材料,在对有限元软件Marc二次开发的基础上,对东江拱坝三级配混凝土单轴试件、三级配混凝土简支梁以及小湾三级配混凝土在静、动荷载作用下的力学性能和破坏过程进行了数值模拟,对试件细观损伤和宏观破坏之间的联系进行了初步探讨。
根据三级配混凝土骨料的实际配比及Walraven公式,计算出混凝土试件中各种粒径骨料的数目,根据蒙特卡罗方法随机确定骨料的空间位置,编制了有关Fortran程序,生成混凝土随机骨料模型。采用Advancing Front方法对随机骨料模型进行网格剖分,网格剖分严格按骨料、界面和砂浆分别进行。对东江拱坝试件在单轴荷载作用下数值模拟时,各相材料的力学参数取为定值,模拟结果表明界面是试件的薄弱环节,试件的微裂纹首先出现在界面单元上,然后向相邻砂浆单元扩张,微裂纹不断扩展、合并,最终导致试件破坏。对三级配混凝土简支梁进行数值模拟时,假定各相材料的抗拉强度和弹性模量服从Weibull、对数正态两种随机分布,其他力学参数取定值,生成和实际结构比较接近的随机骨料随机参数模型,数值模拟结果表明材料均质度较高的试件出现非线性行为的时间要明显滞后于均质度较低的试件;弹性模量分布的随机性对材料线弹性段力学性能的影响极小,而对非线性区域的影响较大;材料强度分布的随机性对混凝土的强度和损伤阈值有较大的影响。三级配混凝土动载数值模拟结果表明,在短时高速的冲击荷载作用下,试件的极限承载力提高,破坏时的位移降低;在没有初始静载的情况下,规范规定的把材料的抗拉强度和弹性模量提高1.3倍所得极限承载力相对较大。最后,对三级配混凝土简支梁三维数值模型进行研究,生成三维随机骨料随机参数模型。数值模拟时假定每个骨料周围界面单元的强度和弹性模量为定值,但不同骨料周围界面单元的强度和弹性模量服从Weibull分布。为了减少计算量,把小骨料和砂浆看作一种材料,用等效夹杂理论对其等效力学参数进行求解,基于Mori—Tanaka方法和二相串连法提出了研究等效力学参数的混合法。空间数值模拟结果和平面结果的比较表明本文的模拟方法是可行的,结果是合理的。
In this paper, concrete was taken as three-phase composites consisting of aggregate, bond and mortar matrix on micro-level. Based on the second development of finite element software Marc, numerical simulation of mechanical performance and failure process was studied for the uniaxial concrete specimen of Dongjiang arch dam, three-graded-concrete supported beam and three-graded-concrete beam of Xiaowan arch dam under static and dynamic load, and the relation of micro-damage and macro-failure were simply discussed.The number of all kinds of aggregate was decided according to the actual gradation of aggregate of three-graded-concrete and Walraven formula. The location of aggregate was random generated by Monte Carlo method, and the random aggregate model was established by the compiled program with Fortran language. The mesh division of aggregate, bond and mortar matrix was carried out respectively by Advancing Front method. Mechanical parameters of each phase material were considered as constant values when the uniaxial concrete specimen were simulated, the results indicate that the bond is weak links, the micro cracks appears in the bond first before they enter the mortar matrix, then the specimen failed because of the expand, combination of micro cracks. The tensile strength and the elastic modulus were assumed to obey Weibull and logarithmic normal distribution and the other mechanical parameters were taken as constant values in the simulations of three-graded-concrete supported beam. The random aggregate random parameters model was established, which is very close to the actual structure. The results show that the nonlinear behavior of higher homogeneous specimen appears later obviously; the influence of random distribution of elastic modulus on the mechanical character is very little in linear range, while great in nonlinear range; random distribution of tensile strength affects the strength and the damage threshold of concrete obviously. The results of simulations of three-graded-concrete supported beam under dynamic load show that in the impact load the carrying capacity improved and the displacement decreased when specimen failed, and without inial static load, it is dangerous that material tensile strength and elastic modulus were improved to its 1.3 times in the code. In the last, the three dimensional random aggregate random parameters model was established. The tensile strength and elastic modulus of bond element surrounding same aggregate were taken as constant value, but those of bond
element surrounding different aggregate were assumed to obey Weibull distribution. In order to reduce the efforts of calculation, small aggregate and mortar were considered as one material and its equivalent mechanical parameters were decided by the method of equivalent inhomogeneity. Based on method of Mori-Tanaka and two-phase tandem method, mixed method was presented to calculate the equivalent mechanical parameters. The comparison between results of three dimensional simulations and those of two dimensional simulations show that the numerical simulation method in this paper is feasible and the results are reasonable.
根据三级配混凝土骨料的实际配比及Walraven公式,计算出混凝土试件中各种粒径骨料的数目,根据蒙特卡罗方法随机确定骨料的空间位置,编制了有关Fortran程序,生成混凝土随机骨料模型。采用Advancing Front方法对随机骨料模型进行网格剖分,网格剖分严格按骨料、界面和砂浆分别进行。对东江拱坝试件在单轴荷载作用下数值模拟时,各相材料的力学参数取为定值,模拟结果表明界面是试件的薄弱环节,试件的微裂纹首先出现在界面单元上,然后向相邻砂浆单元扩张,微裂纹不断扩展、合并,最终导致试件破坏。对三级配混凝土简支梁进行数值模拟时,假定各相材料的抗拉强度和弹性模量服从Weibull、对数正态两种随机分布,其他力学参数取定值,生成和实际结构比较接近的随机骨料随机参数模型,数值模拟结果表明材料均质度较高的试件出现非线性行为的时间要明显滞后于均质度较低的试件;弹性模量分布的随机性对材料线弹性段力学性能的影响极小,而对非线性区域的影响较大;材料强度分布的随机性对混凝土的强度和损伤阈值有较大的影响。三级配混凝土动载数值模拟结果表明,在短时高速的冲击荷载作用下,试件的极限承载力提高,破坏时的位移降低;在没有初始静载的情况下,规范规定的把材料的抗拉强度和弹性模量提高1.3倍所得极限承载力相对较大。最后,对三级配混凝土简支梁三维数值模型进行研究,生成三维随机骨料随机参数模型。数值模拟时假定每个骨料周围界面单元的强度和弹性模量为定值,但不同骨料周围界面单元的强度和弹性模量服从Weibull分布。为了减少计算量,把小骨料和砂浆看作一种材料,用等效夹杂理论对其等效力学参数进行求解,基于Mori—Tanaka方法和二相串连法提出了研究等效力学参数的混合法。空间数值模拟结果和平面结果的比较表明本文的模拟方法是可行的,结果是合理的。
In this paper, concrete was taken as three-phase composites consisting of aggregate, bond and mortar matrix on micro-level. Based on the second development of finite element software Marc, numerical simulation of mechanical performance and failure process was studied for the uniaxial concrete specimen of Dongjiang arch dam, three-graded-concrete supported beam and three-graded-concrete beam of Xiaowan arch dam under static and dynamic load, and the relation of micro-damage and macro-failure were simply discussed.The number of all kinds of aggregate was decided according to the actual gradation of aggregate of three-graded-concrete and Walraven formula. The location of aggregate was random generated by Monte Carlo method, and the random aggregate model was established by the compiled program with Fortran language. The mesh division of aggregate, bond and mortar matrix was carried out respectively by Advancing Front method. Mechanical parameters of each phase material were considered as constant values when the uniaxial concrete specimen were simulated, the results indicate that the bond is weak links, the micro cracks appears in the bond first before they enter the mortar matrix, then the specimen failed because of the expand, combination of micro cracks. The tensile strength and the elastic modulus were assumed to obey Weibull and logarithmic normal distribution and the other mechanical parameters were taken as constant values in the simulations of three-graded-concrete supported beam. The random aggregate random parameters model was established, which is very close to the actual structure. The results show that the nonlinear behavior of higher homogeneous specimen appears later obviously; the influence of random distribution of elastic modulus on the mechanical character is very little in linear range, while great in nonlinear range; random distribution of tensile strength affects the strength and the damage threshold of concrete obviously. The results of simulations of three-graded-concrete supported beam under dynamic load show that in the impact load the carrying capacity improved and the displacement decreased when specimen failed, and without inial static load, it is dangerous that material tensile strength and elastic modulus were improved to its 1.3 times in the code. In the last, the three dimensional random aggregate random parameters model was established. The tensile strength and elastic modulus of bond element surrounding same aggregate were taken as constant value, but those of bond
element surrounding different aggregate were assumed to obey Weibull distribution. In order to reduce the efforts of calculation, small aggregate and mortar were considered as one material and its equivalent mechanical parameters were decided by the method of equivalent inhomogeneity. Based on method of Mori-Tanaka and two-phase tandem method, mixed method was presented to calculate the equivalent mechanical parameters. The comparison between results of three dimensional simulations and those of two dimensional simulations show that the numerical simulation method in this paper is feasible and the results are reasonable.
引文
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[3] 曹礼群.材料物性的多尺度关联与数值模拟[J].世界科技与进展,24(6):23～30
[4] Peterson, P. E. Crack growth and development of fracture zones in plane concrete and similar materials [M]. Lund Institute of Technology, 1981
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[6] Schlangen, E., Garbocai, E. J. Fracture simulations of concrete using lattice models: computional aspects [J]. Engng. Frac. Mech., 1997, 57(2/3): 319～322
[7] 杨强,张浩,周维恒.基于格构模型的岩石类材料破坏过程的数值模拟[J].水利学报,2002,(4):46～50
[8] 杨强,程勇刚,张浩.基于格构模型底岩石类材料开裂数值模拟[J].工程力学,2003,20(1):117～126
[9] 马怀发,陈厚群,黎保琨.混凝土细观力学研究进展及评述[J].中国水利水电科学研究院学报 2004,2(2):124～130
[10] 张德海,邢纪波,朱浮生,杨顺存.混凝土破坏过程的数值模拟.东北大学学报,2004,25(2):175～178
[11] 刘光廷,王宗敏.用随机骨料模型模拟混凝土材料的断裂[J].清华大学学报,1996,36(1):84～89
[12] 宋玉普.多种混凝土材料的本构关系和破坏准则[M].北京:中国水利水电出版社,2002
[13] 黎保琨,彭一江.碾压混凝土试件细观损伤断裂的强度与尺寸效应[J].华北水利水电学院学报,2001,22(3):50～53
[14] 任朝军,杜成斌,戴春霞.三级配混凝土单轴破坏的细观数值模拟[J].河海大学学报,2005,33(2):177～180
[15] 朱万成,唐春安,赵文等.混凝土试样在静态荷载作用下断裂过程的数值模拟研究[J].工程力学,2002,19(6):148～153
[16] 马怀发,陈厚群,黎保琨.应变率效应对混凝土动弯拉强度的影响[J].水利学报,2005,36(1):69～76
[17] Bazant, Z. P., Chen, E. P. Scaling of structural failure. Applied Mechanics Review, 1977, 50(10): 593～627
[18] 王宝庭,宋玉普,张燕坤.基于刚体—弹簧模型的混凝土微裂纹行为模拟[J].大连理工大学学报,1999,16(2):140～144
[19] Wittmann, F. H., Roelfdtra, P. E., SadoukiH. Simulaition and analysis of composite structures [J]. Mater Sci ENGNG, 1984, 68: 239～248.
[20] 王宗敏,不均质材料(混凝土)裂隙扩展及宏观计算强度与变形[D].北京:清华大学,1996
[21] 高政国,刘光廷.二维混凝土随机模型研究[J].清华大学学报,2003,43(5):710-714
[22] 高政国,刘光廷.三维混凝土骨料随机投放算法[J].清华大学学报,2003,43(8):1120～1123。
[23] 孙立国,杜成斌,戴春霞.大体积混凝土随机骨料模型的数值模拟[J].河海大学学报,2005,33(2).
[24] 孙立国.三级配(全级配)混凝土骨料形状的数值模拟及其应用[D].南京:河海大学,2005
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