LAUSR

Abstract An efficient finite element model for two-dimensional (2D) time-dependent chloride diffusion (2D-TCD) was proposed to describe the chloride concentration distribution within the corner and edge areas of concrete members. Governing equation as well as boundary and initial conditions for 2D-TCD were established first. Then the lumped concentration matrix (LCM) for 2D-TCD was derived based on the Galerkin's weighted residual method and the trapezoidal formula. Moreover, an efficient finite element model for 2D-TCD was proposed based on the precise time-integration method and the Pade series expansion technology. Finally, the accuracy and efficiency of the proposed model were validated by comparing with the analytical model, traditional finite element model and experimental data. Analysis shows that the proposed model overcomes the numerical stability problems (such as oscillations and negative values) of traditional models by adopting the LCM to establish finite element equation of 2D chloride diffusion. Meanwhile, the computational accuracy and efficiency of the proposed model are higher than those of the traditional models, since it adopts the Pade series expansion instead of the Taylor series expansion to derive the general solution of 2D chloride diffusion. Moreover, the proposed model can not only balance the computational accuracy, efficiency and numerical stability, but also be insensitive to the meshed sizes of spatial grids and time steps.