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This paper shows how the double-K fracture parameters KIcini and KIcun can be determined for concrete using CT-specimens and wedge splitting specimens. The experimental results collected from the fracture tests the very large size CT-specimens and small size wedge splitting specimens carried out by many researchers are utilized to investigate the characters of the obtained double-K fracture parameters KIcini and KIcun. It was found that the double-K fracture parameters KIcini and KIcun determined from fracture tests on the large size CT-specimens are size-independent. And the values of KIcini and KIcun determined from small size wedge splitting specimens with same dimensions are independent of the relative preformed notch length a0/D. However, when the dimensions of small size wedge splitting specimens change from 150×150×150 mm3 to 450×450×450 mm3, the values of KIcini and KIcun slightly depend on the heights of the specimens and do not depend on the thickness of the specimens.