Abstract:To determine the underlying probabilistic distributions of the physical and mechanical property parameters of the mesoscopic representative volume element (RVE) and to form the probabilistic volume element (PVE) models,it is a quintessential problem in the elastic damage analysis of quasi-brittle materials by means of the damage micromechanics. In particular,it is the theoretical basis of initializing the heterogeneous material properties in the famous finite element micromechanics code,rock failure process analysis (RFPA). The RFPA code and its embedded PVE model based on the Weibull distribution are introduced briefly first. Then other two historical studied PVE models based on the quasi-Weibull distribution and the normal distribution in the theoretical research for building the RFPA code are also described briefly. After the discussion and review of these PVE models in detail,a PVE model based on lognormal distribution is proposed to improve the simulation of the heterogeneity of quasi-brittle materials and to provide an alternative type of PVE model for the RFPA code. The rationality that the heterogeneity of rock-like materials is able to be described by the lognormal distribution is proved by the uncertainty analysis of the influencing factors of material properties. The lognormal PVE model is compared with these three PVE models and is verified with the complete stress-strain curves of various rocks obtained in the laboratory simply uniaxial tests. Comparisons and verifications show that,similar to Weibull distribution,the proposed lognormal distribution is suitable for the PVE modeling and agrees very well with the elastic damage constitutive relationship of quasi-brittle materials. This research also provides a circumstantial evidence that it is reasonable to use Weibull distribution in the PVE modeling and the RFPA code. In the PVE modeling in the statistical elastic damage analysis of quasi-brittle materials,lognormal distribution is an alternative choice besides Weibull distribution,but the normal distribution and the quasi-Weibull distribution should be excluded.