Solving the Chloride Diffusion Equation in Concrete Structures for Prediction of Initiation Time of Corrosion Using The Finite Point Method

Reinforced concrete structures exposed to sea environments suffer from corrosion of steel bars due to the chloride ingress. This corrosion may lead to serious damages to concrete structures and cost of repair, inspection and maintenance activities for these structures could reach a level comparable to the cost of construction of new structures. Therefore, the chloride penetration is a major factor that affects the durability of concrete structures. Diffusion of chloride ions is generally assumed to follow the Fick’s second law [

1

].

In this paper, the finite point method is adopted for solving the chloride diffusion equation for prediction of service life of concrete structures and initiation time of corrosion of reinforcement. Finite point method (FPM) is a truly meshless method which uses a moving least square approximation (MLS) within a collocation strong form for solving the governing differential equation [

2

]. To calculate the derivatives of variables with respect to time, both forward and backward difference methods are used, the former proved to be more accurate and satisfactory. An optimum value for radius of support domain in MLS approximation is obtained in order to achieve more precise results.

Several 1D and 2D problems of chloride diffusion are solved using FPM and the results are compared with the analytical solution, classical finite element and finite difference methods, and weak form meshless based Element Free Galerkin method. 1D tests demonstrated that FPM and FDM provide very close predictions whereas for 2D problems, if regular distribution of nodes are used, the FPM and FDM remain close, while FPM can also be efficiently used for accurate simulation using irregular distribution of nodes and solving complex geometries. Although, it is expected that prediction of the initiation time of corrosion by EFG be much closer to the exact initiation time, nevertheless, it should be noted that the FPM procedure is more straightforward in comparison to EFG and it does not need any integration procedures, making it a simple approach to implement as well as being computationally inexpensive. Furthermore, the comparison of computing time for solving the 2D equation in different methods illustrate that FPM is the fastest computational approach for solving general complex geometries.