Numerical simulation is used to explore the behavior of concrete beams of different sizes and different notch lengths, loaded in three-point bending. The entire range of notch depth is studied. One limit case is type 1 fracture, which occurs when the notch depth is zero and the crack initiates from a smooth surface (this is the case of the modulus of rupture test). Another limit is type 2 fracture, which occurs for deep enough notches. Both cases exhibit very different size effects. The fracture is simulated numerically with a robust mesolevel lattice-particle model. The results shed light on the transitional behavior in which the notch depth is non-zero but not deep enough for developing the the type 2 size effect dominated by energy release from the structure. In agreement with experimental observations and theoretical predictions, the numerical results show evidence of a decreasing macroscopic fracture energy as the ligament gets very short.