Abstract: Geometrically similar specimens and non-geometrically similar specimens are respectively recommended for the size effect model (SEM) and the boundary effect model (BEM). Considering the individual characteristics and advantages of the SEM and BEM, it proposed an improved discrete particle fracture model for concrete. The fracture tests of two types of specimens with geometrical and non-geometrical similarity are used to determine the material parameters of concrete, that is, the fracture toughness and tensile strength. The determined strengths are compared with the experimental strengths. The determined fracture toughness is compared with the values determined by the SEM. The results show that when the ratio of the ligament length (W−a₀) to the representative size of aggregate d_i is approximately 10, the correlation coefficient of the determination curves for the fracture toughness and tensile strength is the best. The determined fracture toughness and tensile strength are in good agreement with the experimental strengths and the fracture toughness from the SEM. Based on the determined concrete material parameters using the geometrically similar, the non-geometrically similar, and the geometrically and non-geometrically similar specimens, the corresponding design curves of concrete under different conditions are established. The design curves can cover all test data by ±20%. Based on a statistical analysis, the fictitious crack growth length Δa_fic=nd_i and the characteristic crack length a_\infty ^ *=0.5d_i can be taken. Then the analytical relations between the peak load and fracture toughness and between the peak load and tensile strength are established. The purpose of directly determining the fracture toughness and tensile strength of concrete using the experimental peak loads is achieved. ±15% of the predicted curves can cover all the experimental data. Based on the analytical formulas, the peak loads of large-scale real concrete structures that exhibit linear elastic fracture can be predicted.