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Based on contact fractal theory and micro-contact size distribution function, a fractal model of normal contact stiffness of joint interfaces was proposed, considering the influence of the domain extension factor for micro-contact size distribution. Furthermore, numerical simulation was carried out to obtain the nonlinear relationships between normal contact stiffness and characteristic parameters of joint interfaces. And the effect of these parameters on the normal contact stiffness was also analysed. The results show that the normal contact stiffness of joint interfaces increases with the normal load on joint interface, decreases with the fractal characteristic length scale parameter G, however, complicatedly varies with the fractal dimension D.