Abstract：Based on the statistical theory and elastic damage theory，constitutive relation of quasi-brittle material model was discussed. Heterogeneity was introduced into the numerical model assigning mechanical parameters throughout the numerical specimens by following Weibull distribution function，normal distribution function，even distribution function or logarithmic normal distribution function. Firstly，heterogeneity index was defined in the models with different distribution functions. By using a numerical code RFPA3D，fracture process of quasi-brittle material was investigated by different statistical distribution functions；and the complete stress-strain curves，peak strength and AE serials were all obtained to analyze the mechanical failure behaviors. The mechanical behaviors obtained in the heterogeneous numerical model implemented by using logarithmic normal distribution function were similar to that in Weibull distribution function. The nonlinear and the brittle failure behaviors become more obvious in more homogeneous models；and the peak strength increases with the homogeneity. Numerical results compared with laboratory test results；and analytical results show both Weibull distribution and logarithmic normal distribution functions are more reasonable and reliable for elastic damage model. Weibull distribution function is the most simple and convenient one among these related distribution functions. Compared with damage model based on statistical theory；numerical modeling is an efficient and convenient method to consider the heterogeneity in many scales and complicated boundary conditions in quasi-brittle materials. The combination of damage theory and computing method is a promising approach to resolve the stochastic problems due to the heterogeneities in quasi-brittle materials.
