Abstract: It presents an improved fracture theory and an associated method for determining the independent material parameters of concrete, e.g. cracking strength, initial fracture toughness, tensile strength and fracture toughness for different types of specimens, in which the heterogeneous properties of concrete were considered. Based on the concrete fracture tests of three-point-bending (3-p-b), wedge-splitting (WS) and four-point-bending (4-p-b) specimens, the corresponding cracking strength, initial fracture toughness, tensile strength and fracture toughness were simultaneously determined. The rationality and applicability of the proposed model and the associated method were verified by the experimental concrete strength and the double K fracture parameters determined by the double K model. The whole initial fracture curves and fracture failure curves of concrete were obtained using the determined materials. The theoretical minimum concrete specimen size for determining the initial fracture toughness to meet the condition of linear elastic fracture mechanics was given. Based on the proposed simple analytic expressions between the cracking strength and the initial fracture toughness, the initial loads of all 3-p-b specimens, WS specimens and 4-p-b specimens were successfully predicted. The initial fracture toughness of concrete was also determined using the analytic expressions.