硫酸盐在圆形混凝土桩中扩散反应解析解

Analytical Solution for Sulfate Diffusion Reaction in Circular Concrete Piles

基于Fick第二定律,建立了硫酸盐在混凝土桩中的扩散反应方程.采用分离变量法和Danckwerts法,结合初始和边界条件,推导出扩散反应方程解析解.进一步考虑硫酸盐侵蚀过程中孔隙填充与膨胀裂缝对硫酸盐扩散系数的影响,提出了混凝土侵蚀劣化全过程有效扩散系数模型.基于硫酸盐扩散反应方程解析解和有效扩散系数模型,获得硫酸盐在混凝土桩中的浓度分布规律,并与试验结果对比,验证了解析解的有效性.算例分析表明:孔隙的填充对硫酸盐扩散的阻碍效果显著,而裂缝的发展促进了硫酸盐的扩散反应;水灰比越小,硫酸盐侵入深度越浅,浓度也越低.

Based on the Fick＇s second law,a diffusion reaction equation of sulfate in concrete piles was established.With the method of separation of variables and Danckwerts,according to initial conditions and boundary conditions,the diffusion reaction equation was deduced.Furthermore,considering the effect of pore filling and crack on diffusion coefficient,an effective diffusion coefficient model was proposed to show the variation of the diffusion coefficient during the degradation process of concrete piles.Sulfate concentration profiles were obtained by the solution and the effective diffusion coefficient model,which agrees well with the experiment data to verify the validity of the proposed analytical solution.Case study shows that the inhibition effect of pore filling on sulfate diffusion is remarkable. The development of the crack promotes the diffusion reaction of sulfate. With water-cement ratio decreasing,the invasion depth of sulfate decreases,as well as the concentration of sulfate in concrete piles.