In this paper, we develop a numerical approach to simulate the 2D complex damage and fracture process of quasi-brittle concrete materials. Based on the phase field theory for the case of elastic isotropic multicomponent materials and the generation process based upon Monte Carlo’s simulation method, we construct a numerical  procedure to solve complex damage thermodynamic problems. The diffusive phase field variable obtained from this calculation can be used to represent the crack nucleation and propagation within 2D complex mesostructure. Some factors that affect the numerical result (type of crack density function and type of split decomposition of strain energy) are accounted to make the predictions more accurate for the case of concrete material. Some new numerical examples are provided to show the usefulness of the approach.

Reinforced concrete has become a widely used construction material around the world. Nowadays, the assessment of deterioration and life expectancy of reinforced concrete structure is very important and necessary as concrete is a complex material with brittle failure. Under the effect of load and over time, cracks occur in the structure, significantly reducing its performance and durability. Therefore, a number of models for predicting the penetration of chloride ions into the concrete were proposed to assess the durability of the structure. In the study performed by T B Viet (2016) [1], the author proposed a new theoretical model, especially considering the effects of macro and micro cracking on the diffusion coefficient of chloride ion in the cracked concrete. The following experimental results, in term of electrical indication of concrete’s ability to resist chloride ion penetration, are used to calculate the lifespan of a reinforced concrete structure according to Dura Crete approach [8] with different crack widths to evaluate the accuracy and reliability of the above model in the range of concrete compressive strength of 30-70MPa.

Effective medium approximations are developed to estimate the macroscopic conductivity of coated-inclusion composites with thin anisotropic coating. The two-phase coated-inclusion are substituted by equivalent one-phase inclusion, using the multi-coated spheres assemblage and the differential substitution approaches. Then, the usual effective medium approximation schemes are applied to the equivalent medium to estimate the conductivity of original three-phase composites. The results obtained were compared with the numerical simulation by finite element method in 2D show the effectiveness of the methods.