Abstract: When the analytical approach is adopted to determine the double-K fracture toughness of concrete, the accuracy of the calculated fracture governing parameter, i.e., the initiation fracture toughness, is directly influenced by the accuracy of the calculated cohesive fracture toughness. An expression for calculating cohesive fracture toughness, where a tension softening relationship determined using CEB-FIP Mode Code is assumed, is developed in the present paper based on the weight function approach. Using the measured maximum loads and critical crack mouth opening displacements of five groups of wedge splitting compact tension specimens of which the maximum depth is 1000mm, the double-K fracture toughness parameters are then evaluated using the developed expression and compared with the values calculated using the analytical integral approach. The results show that two different approaches agree well and the maximum error between them is less than 2%.