数值模拟方法是研究水泥基材料接触溶蚀问题的有效手段,但三维有限元数值模拟问题一直还未得到有效解决,为此,笔者开展了如下研究:①基于质量守恒定律,推导钙离子传输控制方程,并结合固液平衡关系曲线、孔隙率演化模型与有效扩散系数演化模型建立三维钙溶蚀数学模型;引入离子交换边界条件考虑接触边界浓度变化,为钙溶出量计算提供依据;②根据Galerkin有限元方法导出有限元计算格式,实现模型数值求解;通过算例验证,检验三维接触溶蚀模型及程序的正确性。结果表明:该三维模型能够用于模拟水泥基材料发生的多维溶蚀;针对圆柱体试件开展三维溶蚀数值试验,得到了各溶蚀特征量的时空分布规律;在三维状态下,接触溶蚀发展呈现出由表及里,各处溶蚀速率由快到慢,径向溶蚀速率大于轴向溶蚀速率的总体特征。研究结果为水泥基材料的溶蚀影响分析提供了理论基础及方法。
Abstract
Numerical simulation is an effective means to study the contact dissolution of cement-based materials; but the problem regarding its 3D finite element modeling has not been effectively solved. In view of this, attempts were made to build a 3D calcium dissolution model. First of all, the governing equation of calcium ion transmission was deduced in line with the mass conservation law, and on this basis a 3D mathematical model of calcium ion transportation was built based on the solid-liquid equilibrium curve, the porosity evolvement model and the effective diffusion coefficient evolvement model. The ion exchange boundary condition is incorporated to reflect the change of calcium ion concentration at the contact boundary, which provides the basis for calculating the quantity of calcium dissolution. Furthermore, according to the Galerkin finite element method, the finite element computing scheme is derived for numerical solution of the proposed model. The proposed model and FEM program is validated with two examples. Result demonstrates that the proposed model is applicable to simulating the multidimensional contact dissolution of cement-based materials. The spatial distribution and temporal distribution of characteristic variables are obtained by the numerical test of three-dimensional contact dissolution of a cylinder specimen. In 3D state, the contact dissolution develops from the surface to the inside, the dissolution rate varies from fast to slow in the same position, and the radial dissolution rate is larger than axial dissolution rate. The research achievements offer theoretical basis and approach for analyzing the impact of dissolution of cement-based material.
关键词
水泥基材料 /
钙离子传输 /
接触溶蚀 /
溶蚀特征量 /
三维有限元数值模型
Key words
cement-based material /
calcium ion transmission /
contact dissolution /
characteristic dissolution /
three-dimensional finite element model
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参考文献
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