Abstract：The mainly factors affecting overbreak in the tunnels include the geological characteristics of rock mass and geological constitution. The problems of overbreak are met during rock mass excavation. From the mechanism of rock rupture，the fractal dimension of tunnel perimeter is researched on the jointed rock mass. The generalized fractal dimension model of tunnel perimeter in jointed rock mass is put forward；and the relation between affecting parameters and generalized fractal dimension of tunnel perimeter is studied. According to the fractal theory，the relation between overbreak and generalized fractal dimension of tunnel perimeter is built. Based on the geological mechanics mechanism，the relation between overbreak and generalized fractal dimension is built. Finally，an engineering case is used to testify the adaptive of this model. The achieved results show that：(1) the magnitude of generalized fractal dimension model is decided by the characteristics of discontinuity plane during tunnel excavation；(2) it probably produces biggish overbreak due to the biggish fractal dimension；and (3) the quantity of overbreak presents nonlinear increase for many times with relative fractal dimension.
