To clarify the sliding failure mechanism of the shield tunnel face and determine the reasonable range of the supporting force during shield construction

a three-dimensional slip rupture model for the shield tunnel face was proposed by using the spatial discretization technique based on the slip line theory and the upper bound theorem of limit analysis. According to the large principal stress arch theory

the vertical earth pressure at the top of the slip zone was calculated

and the limit supporting force of the tunnel was calculated by using the vertical load on the upper part of the slip damage zone. The results show that the soil arching effect significantly affects the magnitude and the distribution of vertical stress in front of the tunnel face. By comparing proposed model with existing approaches

it is found that the upper bound solution of limit supporting force obtained from the new model has good applicability in both purely cohesive soils and frictional soils. At the same time

the shape of the damaged area on the tunnel face is fairly consistent with the results from the centrifuge model test and numerical calculation.