含裂纹混凝土的三维渗透性分析
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摘要
该文假设含裂纹的混凝土材料是由孔隙基体和裂纹组成的二相复合材料,基于相互作用直推法(IDD)给出了三维周期裂纹渗透性的表达式。基于单元嵌入技术和弹性比拟的数值模拟新方法,解决了三维细观连续有限元实体模型的建模和网格划分问题,实现了含混凝土裂纹的三维渗透模拟。假设裂纹为圆盘状,引入周期性的概念并提出三维周期裂纹结构模型,分析裂纹直径、裂纹周期、裂纹倾角和裂纹间距等因素对整体等效渗透性能的影响。将得到的数值解和IDD理论解进行对比分析,结果表明:在裂纹密度较低时,数值解和理论解吻合得很好,但随着裂纹密度的增大,二者之间的误差逐渐增大;当裂纹趋于连通时,IDD解低估了裂纹之间的近场相互作用而偏离数值解;裂纹接近连通时,整体等效渗透率与裂纹密度呈对数关系,可用渐进对数表达式准确描述。
Concrete with cracks is considered to be a two-phase composite material with a porous matrix and cracks. The interaction direct derivative(IDD) expression was used to estimate the effective permeability of periodic crack model. The conventional seepage numerical analysis method associated with continuous solid elements has some difficulties in mesh coordination, so a new method which combines embedded element technique with elastic analogy was developed to solve this problem. Based on the assumption of penny cracks, a model with three dimensional periodic microstructures was carried out to represent the geometric arrangement of cracks, and the effect of different geometric factors, namely crack diameter, crack density, structure periodicity, crack inclination, and space interval, were studied. The numerical result derived from the new method, was compared with the theoretical solution from IDD. The results reveal that the IDD-derived solution is suitable for low crack density, but it starts to underestimate the finite element results at higher crack density, especially when cracks are nearly touching. During their approach to each other, the effective permeability can be described by an asymptotic logarithmic expression.
Concrete with cracks is considered to be a two-phase composite material with a porous matrix and cracks. The interaction direct derivative(IDD) expression was used to estimate the effective permeability of periodic crack model. The conventional seepage numerical analysis method associated with continuous solid elements has some difficulties in mesh coordination, so a new method which combines embedded element technique with elastic analogy was developed to solve this problem. Based on the assumption of penny cracks, a model with three dimensional periodic microstructures was carried out to represent the geometric arrangement of cracks, and the effect of different geometric factors, namely crack diameter, crack density, structure periodicity, crack inclination, and space interval, were studied. The numerical result derived from the new method, was compared with the theoretical solution from IDD. The results reveal that the IDD-derived solution is suitable for low crack density, but it starts to underestimate the finite element results at higher crack density, especially when cracks are nearly touching. During their approach to each other, the effective permeability can be described by an asymptotic logarithmic expression.
引文
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[22]Fish J.The s-version of the finite element method[J].Computers&Structures,1992,43(3):539―547.
[23]Fish J,Markolefas S,Guttal R,et al.On adaptive multilevel superposition of finite element meshes for linear elastostatics[J].Applied Numerical Mathematics,1994,14(1):135―164.
[24]Joosten M W,Dingle M,Denmead A,et al.Simulation of progressive damage in composites using the enhanced embedded element technique[C]//East Lansing,United States:American Society of Composites-30th Technical Conference,2015:1―27.
[25]Jiang W G,Hallett S R,Wisnom M R.Development of domain superposition technique for the modelling of woven fabric composites[M]//Mechanical Response of Composites,Springer Netherlands,2008:281―291.
[26]曲圣年,焦柯.用固体力学通用程序计算某些流体力学问题[J].水动力学研究与进展,1992(1):110―117.Qu Shengnian,Jiao Ke.Calculating some fluid mechanics problems by the general purpose program of solid mechanics[J].Journal of Hydrodynamics,1992(1):110―117.(in Chinese)
[27]Zheng Q S,Du D X.An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution[J].Journal of the Mechanics and Physics of Solids,2001,49(11):2765―2788.
[28]Du D X,Zheng Q S.A further exploration of the interaction direct derivative(IDD)estimate for the effective properties of multiphase composites taking into account inclusion distribution[J].Acta Mechanica,2002,157(1/2/3/4):61―80.
[29]Deng F,Zheng Q.Interaction models for effective thermal and electric conductivities of carbon nanotube composites[J].Acta Mechanica Solida Sinica,2009,22(1):1―17.
[30]Shafiro B,Kachanov M.Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes[J].Journal of Applied Physics,2000,87(12):8561―8569.
[31]Baecher G B,Lanney N A,Einstein H H.Statistical description of rock properties and sampling[C]//Golden,Colorado,America:The 18th US Symposium on Rock Mechanics(USRMS).American Rock Mechanics Association,1977:1―8.
[32]周春圣.考虑裂纹网络的混凝土多相材料渗透性的理论与试验研究[D].北京:清华大学,2011.Zhou Chunsheng.Theoretical and experimental study on permeability of concrete incorporating cracks network[D].Beijing:Tsinghua University,2011.(in Chinese)
[33]Keller J B.Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders[J].Journal of Applied Physics,1963,34(4):991―993.
[34]Zuzovsky M,Brenner H.Effective conductivities of composite materials composed of cubic arrangements of spherical particles embedded in an isotropic matrix[J].Zeitschrift für angewandte Mathematik und Physik ZAMP,1977,28(6):979―992.
[35]Batchelor G K,O’Brien R W.Thermal or electrical conduction through a granular material[C]//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1977,355(1682):313―333.
[2]Liao K Y,Chang P K,Peng Y N,et al.A study on characteristics of interfacial transition zone in concrete[J].Cement&Concrete Research,2004,34(6):977―989.
[3]周春圣,李克非.含裂纹夹杂多孔材料的渗透性理论与数值分析[J].工程力学,2013,30(4):150―156.Zhou Chunsheng,Li Kefei.Theoretical and numerical analyses of permeability of porous medium with cracking inclusions[J].Engineering Mechanics,2013,30(4):150―156.(in Chinese)
[4]Picandet V,Khelidj A,Bellegou H.Crack effects on gas and water permeability of concretes[J].Cement&Concrete Research,2009,39(6):537―547.
[5]Qian C,Huang B,Wang Y,et al.Water seepage flow in concrete[J].Construction&Building Materials,2012,35(35):491―496.
[6]Akhavan A,Rajabipour F.Quantifying the effects of crack width,tortuosity,and roughness on water permeability of cracked mortars[J].Cement and Concrete Research,2012,42(2):313―320.
[7]Aldea C M,Shah S P,Karr A.Effect of cracking on water and chloride permeability of concrete[J].Journal of Materials in Civil Engineering,1999,11(3):181―187.
[8]Djerbi A,Bonnet S,Khelidj A,et al.Influence of traversing crack on chloride diffusion into concrete[J].Cement and Concrete Research,2008,38(6):877―883.
[9]Reinhardt H W,Jooss M.Permeability and self-healing of cracked concrete as a function of temperature and crack width[J].Cement and Concrete Research,2003,33(7):981―985.
[10]卢子臣,孔祥明,岳蕾,等.水泥石单一裂隙的渗流规律及其遇水自愈合性能[J].硅酸盐学报,2014,42(8):960―965.Lu Zichen,Kong Xiangming,Yue Lei,et al.Water flow through single crack in hardened cement paste and self-healing property of crack[J].Journal of the Chinese Ceramic Society,2014,42(8):960―965.(in Chinese)
[11]翁其能,袁勇,杨红.开裂混凝土衬砌的渗透模型[J].铁道学报,2008,30(2):124―127.Weng Qineng,Yuan Yong,Yang Hong.Permeability model of cracked tunnel lining concrete[J].Journal of the China Railway Society,2008,30(2):124―127.(in Chinese)
[12]Ghasemzadeh F,Pour-Ghaz M.Effect of damage on moisture transport in concrete[J].Journal of Materials in Civil Engineering,2014,27(9):04014242.
[13]Koster M,Hannawald J,Brameshuber W.Simulation of water permeability and water vapor diffusion through hardened cement paste[J].Computational Mechanics,2006,37(2):163―172.
[14]Ammouche A,Riss J,Breysse D,et al.Image analysis for the automated study of microcracks in concrete[J].Cement&Concrete Composites,2001,23(2):267―278.
[15]Litorowicz A.Identification and quantification of cracks in concrete by optical fluorescent microscopy[J].Cement and Concrete Research,2006,36(8):1508―
[16]李曙光,陈改新,鲁一晖.基于数字图像处理的混凝土微裂纹定量分析技术[J].建筑材料学报,2013,16(6):1072―1077.Li Shuguang,Chen Gaixin,Lu Yihui.Automatic quantitative analysis of microcracks in concrete based on digital image processing techniques[J].Journal of Building Materials,2013,16(6):1072―1077.(in Chinese)
[17]Wang L,Ueda T.Mesoscale modelling of the chloride diffusion in cracks and cracked concrete[J].Journal of Advanced Concrete Technology,2011,9(3):241―249.
[18]王立成,鲍玖文.开裂混凝土中水分传输过程的细观模型[J].建筑材料学报,2014,17(6):972―977.Wang Licheng,Bao Jiuwen.Mesoscale model for water transport in cracked concrete[J].Journal of Building Materials,2014,17(6):972―977.(in Chinese)
[19]Chung S Y,Han T S,Kim S Y.Reconstruction and evaluation of the air permeability of a cement paste specimen with a void distribution gradient using CT images and numerical methods[J].Construction and Building Materials,2015,87:45―53.
[20]Promentilla M A B,Cortez S M,Papel R A D C,et al.Evaluation of microstructure and transport properties of deteriorated cementitious materials from their X-ray computed tomography(CT)images[J].Materials,2016,9(5):388.
[21]Tabatabaei S A,Lomov S V,Verpoest I.Assessment of embedded element technique in meso-FE modelling of fibre reinforced composites[J].Composite Structures,2014,107:436―446.
[22]Fish J.The s-version of the finite element method[J].Computers&Structures,1992,43(3):539―547.
[23]Fish J,Markolefas S,Guttal R,et al.On adaptive multilevel superposition of finite element meshes for linear elastostatics[J].Applied Numerical Mathematics,1994,14(1):135―164.
[24]Joosten M W,Dingle M,Denmead A,et al.Simulation of progressive damage in composites using the enhanced embedded element technique[C]//East Lansing,United States:American Society of Composites-30th Technical Conference,2015:1―27.
[25]Jiang W G,Hallett S R,Wisnom M R.Development of domain superposition technique for the modelling of woven fabric composites[M]//Mechanical Response of Composites,Springer Netherlands,2008:281―291.
[26]曲圣年,焦柯.用固体力学通用程序计算某些流体力学问题[J].水动力学研究与进展,1992(1):110―117.Qu Shengnian,Jiao Ke.Calculating some fluid mechanics problems by the general purpose program of solid mechanics[J].Journal of Hydrodynamics,1992(1):110―117.(in Chinese)
[27]Zheng Q S,Du D X.An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution[J].Journal of the Mechanics and Physics of Solids,2001,49(11):2765―2788.
[28]Du D X,Zheng Q S.A further exploration of the interaction direct derivative(IDD)estimate for the effective properties of multiphase composites taking into account inclusion distribution[J].Acta Mechanica,2002,157(1/2/3/4):61―80.
[29]Deng F,Zheng Q.Interaction models for effective thermal and electric conductivities of carbon nanotube composites[J].Acta Mechanica Solida Sinica,2009,22(1):1―17.
[30]Shafiro B,Kachanov M.Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes[J].Journal of Applied Physics,2000,87(12):8561―8569.
[31]Baecher G B,Lanney N A,Einstein H H.Statistical description of rock properties and sampling[C]//Golden,Colorado,America:The 18th US Symposium on Rock Mechanics(USRMS).American Rock Mechanics Association,1977:1―8.
[32]周春圣.考虑裂纹网络的混凝土多相材料渗透性的理论与试验研究[D].北京:清华大学,2011.Zhou Chunsheng.Theoretical and experimental study on permeability of concrete incorporating cracks network[D].Beijing:Tsinghua University,2011.(in Chinese)
[33]Keller J B.Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders[J].Journal of Applied Physics,1963,34(4):991―993.
[34]Zuzovsky M,Brenner H.Effective conductivities of composite materials composed of cubic arrangements of spherical particles embedded in an isotropic matrix[J].Zeitschrift für angewandte Mathematik und Physik ZAMP,1977,28(6):979―992.
[35]Batchelor G K,O’Brien R W.Thermal or electrical conduction through a granular material[C]//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1977,355(1682):313―333.