估算水工結構體內氯離子濃度分佈的數學模型與解析解

Mathematical Model and Its Solution for Estimating the Concentration of Chloride Ions in Hydraulic Structure

鍾文貴(Wen-Guey Chung) ； 陳庭堅(Ting-Chien Chen)

《中國土木水利工程學刊》 23卷2期 (2011/06) Pp. 187-194

https://doi.org/10.6652/JoCICHE.201106_23(2).0006

摘要

水工結構體內氯離子含量是導致鋼筋銹蝕與結構體耐久性劣化的關鍵因素。本文應用拉普拉斯變換與傅立業正弦變換，推導得具Dirichlet條件的一維半無限水工混凝土結構體氯離子傳輸數學模式之基本解，再運用積分技巧求得適用於估算氯離子濃度分佈的幾種邊界條件之解析解，並驗證了解析解的正確性。數值計算結果顯示，解析解中的擴散係數與孔隙水滲透速度對氯離子濃度分佈的影響呈現正比變化，而降解反應係數的影響則呈現反比變化。本文推導得到的解析解，可應用於估算水工結構體內氯離子的濃度分佈，亦可用於驗證電腦模擬混凝土內氯離子複雜傳輸模式數值解的合理性，具有實用價值。

關鍵字

氯離子 ； 解析解 ； 水工結構

並列摘要

The negative influence of chloride on concrete durability has been proved by many researchers. With the aid of both Laplace transform and Fourier Sine transform, the fundamental solution for the chloride ion transport problems with Dirichlet boundary conditions in a semi-infinite saturated, homogeneous hydraulic structure is derived in this paper. The analytical solutions with given boundaries for estimating the distribution of chloride concentration in hydraulic structure are presented. The validity of each solution is analyzed and discussed. Numerical computation shown that diffusion coefficient, reaction coefficient and seepage velocity are three dominant factors for the derived solutions. The concentration of chloride is increasing while the diffusion coefficient or seepage velocity is increasing, but the reaction coefficient is in opposition. The presented solutions are helpful for estimating the chloride concentration in hydraulic structure and can be used for verifying numerical simulations of chloride transport in complex concrete systems.

並列關鍵字

chloride ； analytical solution ； hydraulic structure