A PRACTICAL ANALYTICAL METHOD TO SOLVE EQUIVALENT FRACTURE TOUGHNESS OF CONCRETE BASED ON FICTITIOUS CRACK MODEL
The cohesive strength of the fictitious crack generated by the sub-critical growth of main crack is an important factor affecting the size dependence of the fracture toughness of concrete.According to the fracture property of the quasi-brittle material of concrete,a practical analytical method,to solve the equivalent fracture toughness of concrete is established based on fictitious crack model.At first,according to the basic principles in the composite material mechanics and the linear elastic fracture mechanics,the cohesive strength of the fictitious crack is taken as the boundary condition.Based on the modified shear lag theory and by introducing the variable layer in different zones,the layered shear lag model is built.Then based on the energy law,an analytical form to solve the equivalent fracture toughness of concrete is derived.Finally,against the numerical solutions of the related experiments,the analytical solutions of the equivalent fracture toughness of concrete are obtained.The results show that in the case of varying sub-layers,the mean square deviation and the coefficients of variation of the equivalent fracture toughness of concrete of the volume series specimens are lower than 0.0398 and 0.0384 respectively.The mean square deviation and the coefficients of variation of the height series specimens are lower than 0.0394 and 0.0363 respectively.It proves that the equivalent fracture toughness of concrete is a size-independent fracture parameter.Compared with the numerical solutions,the mean square deviation and the coefficients of variation of the analytical solutions are smaller,which demonstrates that the proposed analytical method is more robust.A conclusion is drawn that the proposed analytical form based on the fictitious crack model provides a reliable and practical analytical method to solve the equivalent fracture toughness of concrete.