Abstract: The shield construction through fault fracture zone is universal,and the existing non-homogeneous model cannot fully respond to the inclination and non-homogeneity of the fault fracture zone. To address this problem,we proposed a spatial non-homogeneous distribution function model. We described the inclination,non-homogeneous and non-homogeneous coefficient size of the fault fragmentation zone by introducing the non-homogeneous direction angle and non-homogeneous coefficient angle,respectively. Then,the model was applied to the limit analysis upper bound method. We derived the calculation formula of the ultimate supporting pressure at the excavation surface of shield tunneling through fault fracture zone. We also verified the rationality of the spatial non-homogeneous distribution function model by calculation examples and engineering examples. Finally,we analyzed the effects of internal friction angle,cohesion,burial depth ratio,and non-homogeneous coefficient on the stability of the excavation surface under different non-homogeneous directions. The results show the follows. The change of the non-homogeneous direction angle has a great influence on the supporting pressure and failure mode of the tunnel excavation surface. The supporting pressure of excavation face decreases with the increase of non-homogeneous direction angle,internal friction angle,cohesion,burial depth ratio and non-homogeneous coefficient. The increase of non-homogeneous directional angle and internal friction angle makes the collapsing body in front of the excavation face change from the trend of sliding downward from the vault to sliding downward from the front. The reinforcement focus should be different for the fault fragmentation zone with different non-homogeneous directional angle and internal friction angle.