EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

混凝土多尺度应力响应方程及其数值模拟

李向南 左晓宝 周广盼 黎亮

李向南, 左晓宝, 周广盼, 黎亮. 混凝土多尺度应力响应方程及其数值模拟. 力学学报, 2022, 54(11): 1-14 doi: 10.6052/0459-1879-22-269
引用本文: 李向南, 左晓宝, 周广盼, 黎亮. 混凝土多尺度应力响应方程及其数值模拟. 力学学报, 2022, 54(11): 1-14 doi: 10.6052/0459-1879-22-269
Li Xiangnan, Zuo Xiaobao, Zhou Guangpan, Li Liang. Equation and numerical simulation on multiscale stress response of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 1-14 doi: 10.6052/0459-1879-22-269
Citation: Li Xiangnan, Zuo Xiaobao, Zhou Guangpan, Li Liang. Equation and numerical simulation on multiscale stress response of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 1-14 doi: 10.6052/0459-1879-22-269

混凝土多尺度应力响应方程及其数值模拟

doi: 10.6052/0459-1879-22-269
基金项目: 国家自然科学基金(52078252)和江苏省自然科学基金项目(BK20200494)
详细信息
    作者简介:

    左晓宝, 教授, 主要研究方向: 混凝土材料与结构. E-mail: xbzuo@sina.com

  • 中图分类号: TU528.1

EQUATION AND NUMERICAL SIMULATION ON MULTISCALE STRESS RESPONSE OF CONCRETE

  • 摘要: 针对混凝土的多相多尺度材料组成特征及其复杂力学响应问题, 首先, 根据混凝土中各组成材料的几何特征, 将C-S-H凝胶、硬化水泥浆体、砂浆及混凝土细观组成分别视为纳观、微观、亚细观和细观尺度上的复合材料, 并利用颗粒空间堆积方法, 重构了混凝土各尺度复合材料的简化几何模型; 其次, 基于重构的几何模型和等效夹杂理论, 通过等效刚度的升阶计算和应力响应的降阶计算, 建立各尺度复合材料应力响应之间的过渡关系, 推导混凝土多尺度应力响应方程, 并编制相应的计算程序; 最后, 以单轴压缩荷载作用为例, 数值计算荷载作用下混凝土各尺度复合材料中的应力响应, 分析骨料空间位置和相互作用以及水化产物刚度、几何形状和空间取向对其应力响应的影响规律. 结果表明, 单轴压缩荷载作用下, 混凝土细观组成中的应力分布并不均匀; 骨料颗粒之间的距离影响到混凝土中的应力分布, 其有效影响范围约为骨料粒径的6倍; 水泥水化产物的刚度、几何形状和空间取向是影响其应力分布的重要因素, 刚度越大, 所受应力越大, 与荷载作用方向的夹角越小, 长椭球形水化产物沿荷载作用方向的应力越大, 扁椭球形水化产物与之相反.

     

  • 图  1  混凝土多尺度代表性体积单元

    Figure  1.  Multiscale representation of concrete

    图  2  等效夹杂理论示意图

    Figure  2.  Schematic of equivalent inclusion theory

    图  3  椭球体夹杂空间位置示意图

    Figure  3.  Schematic of the spatial location of an ellipsoid inclusion

    图  4  混凝土多尺度应力响应的计算框图

    Figure  4.  Flowchart for calculating multiscale stress response of concrete

    图  5  混凝土的细观组成: (a) 粗骨料分布; (b) 有限元网格

    Figure  5.  Meso-concrete: (a) Distribution of aggregate; (b) Finite element mesh

    图  6  截面A-1上应力分布的程序计算值和有限元数值解

    Figure  6.  Program calculation value and finite element solution of stress distribution on section A-1

    图  7  粗骨料和细砂的连续级配曲线

    Figure  7.  Continuous gradation curves of aggregate and fine sand

    图  8  混凝土多尺度几何模型

    Figure  8.  Multiscale geometric model of concrete

    图  9  混凝土细观组成、水泥砂浆和硬化水泥浆体弹性模量随养护时间的变化规律

    Figure  9.  Time-varying elastic modulus of meso-concrete, cement mortar and hardened cement paste

    图  10  截面A-2上各组分的空间分布和应力分布

    Figure  10.  Spatial and stress distribution of each component on section A-2

    图  11  区域B内粗骨料及其周围组分的应力分布

    Figure  11.  Stress distribution of coarse aggregate and its surrounding components in region B

    图  12  细砂中应力随颗粒间距和相对位置的变化

    Figure  12.  The change of normal stress in fine sand particles with the distance and relative position

    图  13  硬化水泥浆体中水泥矿物相及其水化产物所受应力

    Figure  13.  The stress in the cement mineral phase and hydration products in hardened cement paste

    表  1  混凝土中各组分的力学参数

    Table  1.   Mechanical parameters of components in concrete

    ComponentBulk
    modulus/GPa
    Shear
    modulus/GPa
    Source
    C-S-H
    gel
    LD13.98.8[9]
    HD18.811.8[9]
    Cement Mineral PhaseC3S112.551.9[33]
    C2S116.753.8[33]
    C3A120.855.8[33]
    C4AF104.248.1[33]
    Hydration productCH32.514.6[33]
    AFm40.016.0[12]
    AFt14.99.0[12]
    C3AH614.99.0[12]
    C3FH614.99.0[12]
    Fine sand35.925.8[12]
    Coarse aggregate34.330.2[37]
    下载: 导出CSV
  • [1] 过镇海. 钢筋混凝土原理. 北京: 清华大学出版社, 2013

    Guo Zhenhai. Principles of Reinforced Concrete. Beijing: Tsinghua University Press, 2013 (in Chinese))
    [2] 孙伟. 现代结构混凝土耐久性评价与寿命预测. 北京: 中国建筑工业出版社, 2015

    Sun Wei. Durability Evolution and Service Life Prediction of Modern Concrete. Beijing: China Architecture and Building Press, 2015 (in Chinese))
    [3] 缪昌文, 顾祥林, 张伟平, 等. 环境作用下混凝土结构性能演化与控制研究进展. 建筑结构学报. 2019, 40(01): 1-10

    Miao Changwen, Gu Xianglin, Zhang Weiping, et al. State-of-the-art on performance evolution and control of concrete structures subjected to environmental actions. Journal of Building Structures, 2019, 40(01): 1-10(in Chinese)
    [4] Czajkowska J, Malarski M, Witkowska-Dobrev J, et al. Mechanical performance of concrete exposed to sewage-The influence of time and pH. Minerals, 2021, 11(5): 544 doi: 10.3390/min11050544
    [5] 金浏, 李健, 余文轩, 等. 混凝土动态双轴拉压破坏准则细观数值模拟研究. 力学学报, 2022, 54(3): 800-809 doi: 10.6052/0459-1879-21-563

    Jin Liu, Li Jian, Yu Wenxuan, et al. Mesoscopic numerical simulation on dynamic biaxial tension compression failure criterion of concrete. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 800-809(in Chinese) doi: 10.6052/0459-1879-21-563
    [6] Xiao JZ, Zhang KJ, Zhang QT. Strain rate effect on compressive stress-strain curves of recycled aggregate concrete with seawater and sea sand. Construction and Building Materials, 2021, 300: 124014 doi: 10.1016/j.conbuildmat.2021.124014
    [7] 金浏, 李健, 余文轩, 等. 考虑骨料粒径影响的混凝土拉伸强度尺寸效应律. 北京工业大学学报, 2021, 47(04): 311-320 doi: 10.11936/bjutxb2020100009

    Jin Liu, Li Jian, Yu Wenxuan, et al. Size effect law of concrete tensile strength considering the influence of aggregate size. Journal of Beijing University of Technology, 2021, 47(04): 311-320(in Chinese) doi: 10.11936/bjutxb2020100009
    [8] Bernard O, Ulm F, Lemarchand E. A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials. Cement and Concrete Research, 2003, 33(9): 1293-1309 doi: 10.1016/S0008-8846(03)00039-5
    [9] Ulm FJ, Constantinides G, Heukamp FH. Is concrete a poromechanics materials? A multiscale investigation of poroelastic properties. Materials and structures, 2004, 37(1): 43-58 doi: 10.1007/BF02481626
    [10] Pichler B, Hellmich C. Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model. Cement and Concrete Research, 2011, 41(5): 467-476 doi: 10.1016/j.cemconres.2011.01.010
    [11] Stora E, He QC, Bary B. Influence of inclusion shapes on the effective linear elastic properties of hardened cement pastes. Cement and Concrete Research, 2006, 36(7): 1330-1344 doi: 10.1016/j.cemconres.2006.02.007
    [12] Termkhajornkit P, Vu QH, Barbarulo R, et al. Dependence of compressive strength on phase assemblage in cement pastes: Beyond gel-space ratio-Experimental evidence and micromechanical modeling. Cement and Concrete Research, 2014, 56: 1-11 doi: 10.1016/j.cemconres.2013.10.007
    [13] Königsberger M, Hlobil M, Delsaute B, et al. Hydrate failure in ITZ governs concrete strength: A micro-to-macro validated engineering mechanics model. Cement and Concrete Research, 2018, 103: 77-94 doi: 10.1016/j.cemconres.2017.10.002
    [14] Li Y, Liu YZ, Li YN, et al. Evaluation of concrete creep properties based on indentation test and multiscale homogenization method. Cement and Concrete Composites, 2021, 123: 104135 doi: 10.1016/j.cemconcomp.2021.104135
    [15] 潘子超, 阮欣, 陈艾荣. 基于任意级配的二维随机骨料生成办法, 同济大学学报(自然科学版), 2013, 41(05): 759-764

    Pan Zichao, Ruan Xin, Chen Airong. Simulation method of random aggregate in two dimension based on arbitrary gradation. Journal of Tongji University (Natural Science), 2013, 41(05): 759-764(in Chinese)
    [16] 姚泽良, 段东旭, 党发宁, 等. 基于随机骨料模型的再生混凝土单轴压缩数值模拟. 西安理工大学学报, 2018, 34(04): 474-480

    Yao Zeliang, Duan Dongxu, Dang Faning, et al. Numerical simulation of recycled concrete under uniaxial compression based on random aggregate model. Journal of Xi’an University of Technology, 2018, 34(04): 474-480(in Chinese)
    [17] 唐欣薇, 张楚汉. 基于均匀化理论的混凝土宏细观力学特性研究. 计算力学学报, 2009, 26(06): 876-881

    Tang Xinwei, Zhang Chuhan. Study on concrete in macro- and meso-scale mechanical properties based on homogenization theory. Chinese Journal of Computational Mechanics, 2009, 26(06): 876-881(in Chinese)
    [18] Nežerka V, Hrbek V, Prošek Z, et al. Micromechanical characterization and modeling of cement pastes containing waste marble powder. Journal of Cleaner Production, 2018, 195: 1081-1090 doi: 10.1016/j.jclepro.2018.05.284
    [19] 朱合华, 陈庆. 多相材料有效性能预测的高精度方法. 力学学报, 2017, 49(1): 41-47 doi: 10.6052/0459-1879-16-347

    Zhu Hehua, Chen Qing. An approach for predicting the effective properties of multiphase composite with high accuracy. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(1): 41-47(in Chinese) doi: 10.6052/0459-1879-16-347
    [20] 邓方茜, 徐礼华, 池寅, 等. 基于均匀化理论的混杂纤维混凝土有效弹性模量计算. 硅酸盐学报, 2019, 47(02): 161-170

    Deng Fangqian, Xu Lihua, Chi Yin, et al. Calculation of effective elastic modulus for hybrid fiber reinforced concrete based on homogenization theory. Journal of The Chinese Ceramic Society, 2019, 47(02): 161-170(in Chinese)
    [21] Holmes N, Kelliher D, Tyrer M. Simulating cement hydration using HYDCEM. Construction and Building Materials, 2020, 239: 117811 doi: 10.1016/j.conbuildmat.2019.117811
    [22] Zhang ZQ, Liu Y, Huang L, et al. A new hydration kinetics model of composite cementitious materials, Part 1: Hydration kinetic model of Portland cement. Journal of the American Ceramic Society, 2020, 103(3): 1970-1991 doi: 10.1111/jace.16845
    [23] 孙国文, 孙伟, 张云升, 等. 硅酸盐水泥水化产物体积分数定量计算. 东南大学学报(自然科学版), 2011, 41(03): 606-610 doi: 10.3969/j.issn.1001-0505.2011.03.034

    Sun Guowen, Sun Wei, Zhang Yunsheng, et al. Quantitative calculation on volume fraction of hydrated products in Portland cement. Journal of Southeast University, 2011, 41(03): 606-610(in Chinese) doi: 10.3969/j.issn.1001-0505.2011.03.034
    [24] Xu WX, Chen HS. Microstructural characterization of fresh cement paste via random packing of ellipsoidal cement particles. Materials Characte- rization, 2012, 66: 16-23 doi: 10.1016/j.matchar.2012.01.012
    [25] Liu L, Shen DJ, Chen HS, et al. Aggregate shape effect on the diffusivity of mortar: A 3D numerical investigation by random packing models of ellipsoidal particles and of convex polyhedral particles. Computers and Structures, 2014, 144: 40-51 doi: 10.1016/j.compstruc.2014.07.022
    [26] Rodrigues EA, Gimenes M, Bitencourt Jr LAG, et al. A concurrent multiscale approach for modeling recycled aggregate concrete. Construction and Building Materials, 2021, 267: 121040
    [27] Ju C, Ju J W, Chen T M, et al. Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part I:micromechanics-based formulation. International Journal of Solids and Structures, 2001, 38(2): 183-201
    [28] Zaoui A. Continuum Micromechanics: Survey. Journal of Engineering Mechanics, 2002, 128(8): 808-816 doi: 10.1061/(ASCE)0733-9399(2002)128:8(808)
    [29] Zhong X, Dabrowski M, Jamtveit B. Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host. Solid Earth, 2021, 12(4): 817-833 doi: 10.5194/se-12-817-2021
    [30] 陈玉丽, 马勇, 潘飞, 等. 多尺度复合材料力学研究进展. 固体力学学报, 2018, 39(01): 1-68

    Chen Yuli Ma Yong, Pan Fei, et al. Research progress in multi-scale mechanics of composite materials. Chinese Journal of Solid Mechanics, 2018, 39(01): 1-68(in Chinese)
    [31] Eberhardsteiner L, Füssl J, Hofko B, et al. Influence of asphaltene content on mechanical bitumen behavior: experimental investigation and micromechanical modeling, Materials and Structures, 2015, 48(10): 3099-3112
    [32] Zhu QZ, Kondo D, Shao JF. Micromechanical analysis of coupling between anisotropic damage and friction in quasi brittle materials: Role of the homogenization scheme. International Journal of Solids and Structures, 2008, 45(5): 1385-1405 doi: 10.1016/j.ijsolstr.2007.09.026
    [33] Ghabezloo S. Association of macroscopic laboratory testing and micromechanics modelling for the evaluation of the poroelastic parameters of a hardened cement paste. Cement and Concrete Research, 2010, 40(8): 1197-1210 doi: 10.1016/j.cemconres.2010.03.016
    [34] Herve E, Zaoui A. N-Layered inclusion-based micromechanical modelling. International Journal of Engineering Science, 1993, 31(1): 1-10 doi: 10.1016/0020-7225(93)90059-4
    [35] Liu C, Zhang MZ. Effect of curing temperature on hydration, micro-structure and ionic diffusivity of fly ash blended cement paste: A model-ling study. Construction and Building Materials, 2021, 297: 123834 doi: 10.1016/j.conbuildmat.2021.123834
    [36] 金浏, 余文轩, 杜修力, 等. 基于细观模拟的混凝土动态压缩强度尺寸效应研究, 工程力学, 2019, 36(11): 50-61

    Jin Liu, Yu Wenxuan, Du Xiuli, et al. Research on size effect of dynamic compressive strength of concrete based on meso-scale simulation. Engineering Mechanics, 2019, 36(11): 50-61(in Chinese)
    [37] 田梦云, 张恩, 曹瑞东, 等. 基于细观尺度的混凝土单轴力学性能仿真计算分析. 应用力学学报, 2020, 37(03): 975-981

    Tian Mengyun, Zhang En, Cao Ruidong, et al. Meso-scale simulation analysis of uniaxial mechanical behavior of concrete. Chinese Journal of Applied Mechanics, 2020, 37(03): 975-981(in Chinese)
    [38] Chi L, Li WD, Li ZM, et al. Investigation of the hydration properties of cement with EDTA by alternative current impedance spectroscopy. Cement and Concrete Composites, 2022, 126: 104365 doi: 10.1016/j.cemconcomp.2021.104365
    [39] Li Y, Liu YZ, Wang R. Evaluation of the elastic modulus of concrete based on indentation test and multi-scale homogenization method. Journal of Building Engineering, 2021, 43: 102758 doi: 10.1016/j.jobe.2021.102758
    [40] Jin YD, Li L, Jia Y, et al. Numerical study of shrinkage and heating induced cracking in concrete materials and influence of inclusion stiffness with Peridynamics method. Computers and Geotechnics, 2021, 133: 103998 doi: 10.1016/j.compgeo.2021.103998
  • 加载中
图(13) / 表(1)
计量
  • 文章访问数:  23
  • HTML全文浏览量:  5
  • PDF下载量:  3
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-06-14
  • 录用日期:  2022-09-14
  • 网络出版日期:  2022-09-14

目录

    /

    返回文章
    返回