Multi-scale numerical model for simulating concrete material based on fractal theory

A new multi-scale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete. The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced. And the evolutionary process of elastic modulus and strength in small scale is given. Consequently, the multi-scale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale. A two-dimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed. The propagation of cracks of the concrete block is also studied.