This paper shows how the double-K fracture parameters Kini Ic and Kun Ic can be determined for concrete using CT-specimens and wedge splitting specimens. The experimental results collected from the fracture tests on 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 Kini Ic and Kun Ic. It was found that the double-K fracture parameters Kini Ic and Kun Ic determined from fracture tests on the large size CT-specimens are size-independent. And the values of Kini Ic and Kun Ic 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