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Based on the modified MB fractal model and mechanism of contact normal damping dissipating energy, a fractal model of normal damping of joint interfaces was proposed. Furthermore, numerical simulation revealed that the micro concave nonlinear relation of normal damping versus dimensionless total normal load was very evident, which decreased with increasing fractal dimension and normal total load, and increased with increasing fractal scale parameter in the smaller fractal dimension. Besides, the micro convex nonlinear relation of normal damping versus dimensionless total normal load was also very evident, which increased with increasing fractal dimension and normal total load, and decreased with increasing fractal scale parameter in the larger fractal dimension. But the micro concave nonlinear relation of normal dissipation factor versus dimensionless total normal load was very evident, which decreased with increasing normal total load, and increased with increasing fractal scale parameter and fractal dimension. 