The apparent size effect of the specific fracture energy of concrete according to the RILEM procedure has been confirmed by numerous published works. The paper offers an explanation for this size effect by considering the specimen boundary influence on local fracture energy over the ligament length, which is closely associated with the measured fracture energy of concrete. To address this boundary influence, boundary affected length is introduced, over which local fracture energy is different from that in the bulk far away from the surface of the specimen. Based on previous work, a continuous smooth function is hypothesized to simulate the distribution of local fracture energy. At the same time, the model established was compared to the existing models, i.e. Perturbed Ligament Model (PLM) and Bilinear Model (BLM). Some test results from wedge splitting specimen in the literature were used to verify these three models. The results show that the true fracture energy of concrete, irrespective of the specimen size, could be obtained from the measured values directly from RILEM, and is less sensitive to determination approach. The predicted boundary affected length when the crack reaches the specimen surface is more close to the value of the perturbation length in PLM.