Keywords: concrete, diffusion, service life, Fick's second low, mesh free, moving least square method, element free Galerkin method, finite element method, finite difference method.

Reinforced concrete structures exposed to sea environment conditions suffer from corrosion of steel bars due to chloride ingress. It is generally assumed that the diffusion of chloride ions follows the Fick's second low [1,2]. Traditionally, such partial differential equations are solved using numerical methods, such as Finite Element Method (FEM) and Finite Difference Method (FDM). Although these methods are robust and efficient, they exhibit some numerical errors. In the present research, to decrease the numerical errors, Lagrange multiplier element-free Galerkin (EFG) method is applied to the partial differential equation of the Chloride diffusion. In this method, Moving Least Square (MLS) approximation is used to interpolate the field variable for a weak formulation of the boundary value problem [3]. This approximation results continuity to the independent field variable, chloride content, and its gradient in the entire domain. In the present research, first the optimum scaling parameter of the support domain () and the weight function's dilation parameter () in EFG method, which minimizes the displacement error () and energy error () [1] in 1D problem, are found and then the results, errors and predicted service life, are compared with the FE, the FD, and the available analytical solutions in special and practical situations.

It was shown that the EFG method predicts the service life better than other methods and exhibits the minimum displacement error and energy error in the special situation that analytical solution is available and these errors could be found. The FDM performs and its displacement error does not differ considerably with the EFG method. So FDM could compete with EFG method to some extent. The FEM could be used whenever the structure is divided to sufficient elements and its convergence must be always controlled. This study is for the partial differential equation of the Chloride diffusion which is parabolic. The initial boundary value problem may also be used for many other physical phenomena like soil consolidation, heat transfer and others.

1

Oh, B.H., Jang, B.S., "Chloride Diffusion Analysis of Concrete Structures Considering the Effects of Reinforcements", ACI Material Journal, V. 100, No. 2 (2003-03)

2

Goltermann, P., "Chloride Ingress in Concrete Structures; Extrapolation of Observations", ACI Materials Journal: V.100, No.2 (2003-03)

3

Viana, S.A., Mesquita, R.C., "Moving Least Square Reproducing Kernel Method For Electromagnetic Field Computation", IEEE Transactions on Magnetic, vol. 35, No. 3, May 1999. doi:10.1109/20.767218

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