水泥基材料渗透溶蚀有限元模拟方法
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摘要
渗透溶蚀现象在国内外水利工程中大量存在,但对其研究的手段迄今为止还比较单一,为此,探讨采用有限元计算方法研究水泥基材料的渗透溶蚀现象。首先,基于离子在水泥基材料中的水动力弥散与对流作用机理,根据离子质量守恒定律、Fick第二定律、多孔介质渗流数学模型及达西定律建立三维渗透溶蚀过程中钙离子迁移数学模型;然后,结合钙离子迁移数学模型、固液平衡关系、孔隙率演化模型及扩散系数演化模型建立渗透溶蚀数学模型,并给出该模型的有限元计算方法;最后,通过对高水力梯度下的渗透溶蚀试验开展数值模拟,检验渗透溶蚀模型的正确性。计算结果与试验数据基本吻合,表明该方法能够用于模拟水泥基材料的渗透溶蚀过程。所做的研究工作为下一步水利工程中的渗透溶蚀模拟研究奠定了基础,对水利工程的结构安全性研究具有重要意义。
Leakage dissolution which exists extensively in water conservancy projects in China and abroad has not been well revealed by numerical simulation. In view of this, with respect to leakage dissolution of cement-based materials, a research on finite element analysis method is conducted. Firstly, on the basis of the mechanism of hydrodynamic dispersion and convection of ions in cement-based materials, a three-dimensional mathematical model of Ca~(2+) ion transport during leakage dissolution is developed according to the mass conservation law of ion, the Fick's second law, mathematical model of flow in porous media and Darcy's law. In subsequence, a three-dimensional mathematical model of leakage dissolution of cement-based materials is established based on the aforementioned Ca~(2+) ion transportat model, the solid-liquid equilibrium curve, the porosity evolvement model and the diffusion coefficient evolvement model. Meanwhile, the finite element method for this model is given. Finally, the proposed model is validated by numerical simulation of leakage dissolution test under high hydraulic gradient. The simulated result is consistent with the experimental result, which demonstrates that the proposed model can be used to simulate the process of leakage dissolution of cement-based materials. The research lay a foundation for the modeling of leakage dissolution in water resources and hydropower engineering, and is of great significance to the study of structural safety of water resources and hydropower projects.
Leakage dissolution which exists extensively in water conservancy projects in China and abroad has not been well revealed by numerical simulation. In view of this, with respect to leakage dissolution of cement-based materials, a research on finite element analysis method is conducted. Firstly, on the basis of the mechanism of hydrodynamic dispersion and convection of ions in cement-based materials, a three-dimensional mathematical model of Ca~(2+) ion transport during leakage dissolution is developed according to the mass conservation law of ion, the Fick's second law, mathematical model of flow in porous media and Darcy's law. In subsequence, a three-dimensional mathematical model of leakage dissolution of cement-based materials is established based on the aforementioned Ca~(2+) ion transportat model, the solid-liquid equilibrium curve, the porosity evolvement model and the diffusion coefficient evolvement model. Meanwhile, the finite element method for this model is given. Finally, the proposed model is validated by numerical simulation of leakage dissolution test under high hydraulic gradient. The simulated result is consistent with the experimental result, which demonstrates that the proposed model can be used to simulate the process of leakage dissolution of cement-based materials. The research lay a foundation for the modeling of leakage dissolution in water resources and hydropower engineering, and is of great significance to the study of structural safety of water resources and hydropower projects.
引文
[1] 李新宇,方坤河.水工碾压混凝土接触溶蚀特性研究[J].混凝土,2002,(12):12-17.
[2] 莫斯克文 B·M.混凝土和钢筋混凝土的腐蚀及其防护方法[M].北京:化学工业出版社,1988.
[3] 赵铁军.混凝土渗透性[M].北京:科学出版社,2006.
[4] 汝乃华.大坝事故与安全[M].北京:中国水利水电出版社,1995.
[5] ANAND B,SHARMA S N,PATHAK R P,et al.Impact of Soft Water Attack on DAM Concrete[J].International Journal of Emerging Technology and Advanced Engineering,2015,5(3):357-363.
[6] 李新宇.水工混凝土溶蚀特性研究进展与评述[C]//第七届全国混凝土耐久性学术交流会论文集.宜昌:中国土木工程学会混凝土与预应力混凝土分会,2008:70-77.
[7] 朴龙泽,赵淑明,高伟平.丰满大坝渗水对混凝土的溶蚀分析[J].水利水电技术,2000,31(10):34-36.
[8] CARDE C,FRANQOIS R.Effect of the Leaching of Calcium Hydroxide from Cement Paste on Mechanical and Physical Properties[J].Cement and Concrete Research,1997,27(4):539-550.
[9] CARDE C,FRANOIS R.Modelling the Loss of Strength and Porosity Increase Due to the Leaching of Cement Pastes[J].Cement and Concrete Composites,1999,21(3):181-188.
[10] 盛金昌,贾春兰,张羽,等.水工混凝土渗流侵蚀渗透试验研究[J].水力发电学报,2013,32(6):216-221.
[11] HAGA K,SUTOU S,HIRONAGA M,et al.Effects of Porosity on Leaching of Ca from Hardened Ordinary Portland Cement Paste[J].Cement and Concrete Research,2004,35(9):1764-1775.
[12] 方坤河,阮燕,吴玲.混凝土的渗透溶蚀特性研究[J].水力发电学报,2001,1(1):31-39.
[13] 李新宇,方坤河.水工碾压混凝土渗透溶蚀特性研究[J].长江科学院院报,2003,20(3):27-31.
[14] 孔祥芝,纪国晋,刘艳霞,等.水工混凝土渗透溶蚀试验研究[J].中国水利水电科学研究院学报,2012,10(1):63-68.
[15] ADINARAYANA K N V,SASIDHAR P,BALASUBRAMANIYAN V.Modelling of Calcium Leaching and Its Influence on Radionuclide Migration across the Concrete Engineered Barrier in a NSDF[J].Journal of Environmental Radioactivity,2013,124:93-100.
[16] JOHANNESSON B.Nonlinear Transient Phenomena in Porous Media with Special Regard to Concrete and Durability[J].Advanced Cement Based Materials,1997,6(3/4):71-75.
[17] 李新宇,方坤河.混凝土渗透溶蚀过程中钙离子迁移过程数值模拟[J].长江科学院院报,2008,25(6):96-100.
[18] SCHIOPU N,TIRUTA-BARNA L,JAYR E,et al.Modelling and Simulation of Concrete Leaching under Outdoor Exposure Conditions[J].Science of The Total Environment,2009,407(5):1613-1630.
[19] 马强,左晓宝,汤玉娟.环境水侵蚀下水泥净浆钙溶蚀的模拟与验证[J].水利水运工程学报,2017,(3):107-115.
[20] REARDON E J.An Ion Interaction Model for the Determination of Chemical Equilibria in Cement/Water Systems[J].Cement and Concrete Research,1989,20(2):175-192.
[21] BERNER U R.Evolution of Pore Water Chemistry during Degradation of Cement in a Radioactive Waste Repository Environment[J].Waste and Management,1992,12(2):201-219.
[22] WAN K,LI Y,SUN W.Experimental and Modelling Research of the Accelerated Calcium Leaching of Cement Paste in Ammonium Nitrate Solution[J].Construction and Building Materials,2013,40:832-846.
[23] BEJAOUI S,BARY B.Modeling of the Link between Microstructure and Effective Diffusivity of Cement Pastes Using a Simplified Composite Model[J].Cement and Concrete Research,2007,37(3):469-480.
[24] NAKARAI K,ISHIDA T,MAEKAWA K.Modeling of Calcium Leaching from Cement Hydrates Coupled with Micro-pore Formation[J].Journal of Advanced Concrete Technology,2006,4(3):395-407.
[25] DE LARRARD T,BENBOUDJEMA F,COLLIAT J B,et al.Concrete Calcium Leaching at Variable Temperature:Experimental Data and Numerical Model Inverse Identification[J].Computational Materials Science,2010,49(1):35-45.
[26] NGUYEN V H,NEDJAR B,COLINA H,et al.A Separation of Scales Homogenization Analysis for the Modelling of Calcium Leaching in Concrete[J].Computer Methods in Applied Mechanics and Engineering,2006,195(52):7196-7210.
[27] 欧阳华江,肖丁.一类抛物型方程有限元算法的计算准则[J].应用数学和力学,1989,10(12):1115-1121.
[28] 张柔雷,余颖禾.有限元法求解暂态温度场中阶跃现象的分析[J].南京工学院学报,1983,13(3):102-107.
[29] 刘刚,李长生,刘相华.有限元法求解瞬态温度场时的振荡问题[J].钢铁研究学报,2008,20(7):19-22.
[30] 纪峥.关于瞬态温度场有限元分析中采用协调或集中质里热容矩阵的探讨[J].计算力学学报,1986,3(2):38-44.
[31] MAINGUY M,TOGNAZZI C,TORRENTI J,et al.Modelling of Leaching in Pure Cement Paste and Mortar[J].Cement and Concrete Research,2000,30(1):83-90.
[2] 莫斯克文 B·M.混凝土和钢筋混凝土的腐蚀及其防护方法[M].北京:化学工业出版社,1988.
[3] 赵铁军.混凝土渗透性[M].北京:科学出版社,2006.
[4] 汝乃华.大坝事故与安全[M].北京:中国水利水电出版社,1995.
[5] ANAND B,SHARMA S N,PATHAK R P,et al.Impact of Soft Water Attack on DAM Concrete[J].International Journal of Emerging Technology and Advanced Engineering,2015,5(3):357-363.
[6] 李新宇.水工混凝土溶蚀特性研究进展与评述[C]//第七届全国混凝土耐久性学术交流会论文集.宜昌:中国土木工程学会混凝土与预应力混凝土分会,2008:70-77.
[7] 朴龙泽,赵淑明,高伟平.丰满大坝渗水对混凝土的溶蚀分析[J].水利水电技术,2000,31(10):34-36.
[8] CARDE C,FRANQOIS R.Effect of the Leaching of Calcium Hydroxide from Cement Paste on Mechanical and Physical Properties[J].Cement and Concrete Research,1997,27(4):539-550.
[9] CARDE C,FRANOIS R.Modelling the Loss of Strength and Porosity Increase Due to the Leaching of Cement Pastes[J].Cement and Concrete Composites,1999,21(3):181-188.
[10] 盛金昌,贾春兰,张羽,等.水工混凝土渗流侵蚀渗透试验研究[J].水力发电学报,2013,32(6):216-221.
[11] HAGA K,SUTOU S,HIRONAGA M,et al.Effects of Porosity on Leaching of Ca from Hardened Ordinary Portland Cement Paste[J].Cement and Concrete Research,2004,35(9):1764-1775.
[12] 方坤河,阮燕,吴玲.混凝土的渗透溶蚀特性研究[J].水力发电学报,2001,1(1):31-39.
[13] 李新宇,方坤河.水工碾压混凝土渗透溶蚀特性研究[J].长江科学院院报,2003,20(3):27-31.
[14] 孔祥芝,纪国晋,刘艳霞,等.水工混凝土渗透溶蚀试验研究[J].中国水利水电科学研究院学报,2012,10(1):63-68.
[15] ADINARAYANA K N V,SASIDHAR P,BALASUBRAMANIYAN V.Modelling of Calcium Leaching and Its Influence on Radionuclide Migration across the Concrete Engineered Barrier in a NSDF[J].Journal of Environmental Radioactivity,2013,124:93-100.
[16] JOHANNESSON B.Nonlinear Transient Phenomena in Porous Media with Special Regard to Concrete and Durability[J].Advanced Cement Based Materials,1997,6(3/4):71-75.
[17] 李新宇,方坤河.混凝土渗透溶蚀过程中钙离子迁移过程数值模拟[J].长江科学院院报,2008,25(6):96-100.
[18] SCHIOPU N,TIRUTA-BARNA L,JAYR E,et al.Modelling and Simulation of Concrete Leaching under Outdoor Exposure Conditions[J].Science of The Total Environment,2009,407(5):1613-1630.
[19] 马强,左晓宝,汤玉娟.环境水侵蚀下水泥净浆钙溶蚀的模拟与验证[J].水利水运工程学报,2017,(3):107-115.
[20] REARDON E J.An Ion Interaction Model for the Determination of Chemical Equilibria in Cement/Water Systems[J].Cement and Concrete Research,1989,20(2):175-192.
[21] BERNER U R.Evolution of Pore Water Chemistry during Degradation of Cement in a Radioactive Waste Repository Environment[J].Waste and Management,1992,12(2):201-219.
[22] WAN K,LI Y,SUN W.Experimental and Modelling Research of the Accelerated Calcium Leaching of Cement Paste in Ammonium Nitrate Solution[J].Construction and Building Materials,2013,40:832-846.
[23] BEJAOUI S,BARY B.Modeling of the Link between Microstructure and Effective Diffusivity of Cement Pastes Using a Simplified Composite Model[J].Cement and Concrete Research,2007,37(3):469-480.
[24] NAKARAI K,ISHIDA T,MAEKAWA K.Modeling of Calcium Leaching from Cement Hydrates Coupled with Micro-pore Formation[J].Journal of Advanced Concrete Technology,2006,4(3):395-407.
[25] DE LARRARD T,BENBOUDJEMA F,COLLIAT J B,et al.Concrete Calcium Leaching at Variable Temperature:Experimental Data and Numerical Model Inverse Identification[J].Computational Materials Science,2010,49(1):35-45.
[26] NGUYEN V H,NEDJAR B,COLINA H,et al.A Separation of Scales Homogenization Analysis for the Modelling of Calcium Leaching in Concrete[J].Computer Methods in Applied Mechanics and Engineering,2006,195(52):7196-7210.
[27] 欧阳华江,肖丁.一类抛物型方程有限元算法的计算准则[J].应用数学和力学,1989,10(12):1115-1121.
[28] 张柔雷,余颖禾.有限元法求解暂态温度场中阶跃现象的分析[J].南京工学院学报,1983,13(3):102-107.
[29] 刘刚,李长生,刘相华.有限元法求解瞬态温度场时的振荡问题[J].钢铁研究学报,2008,20(7):19-22.
[30] 纪峥.关于瞬态温度场有限元分析中采用协调或集中质里热容矩阵的探讨[J].计算力学学报,1986,3(2):38-44.
[31] MAINGUY M,TOGNAZZI C,TORRENTI J,et al.Modelling of Leaching in Pure Cement Paste and Mortar[J].Cement and Concrete Research,2000,30(1):83-90.