Wedge model has been widely used in the calculation of the limit supporting pressure of shield tunnel excavation face due to its simple and intuitive

but the determination of sliding face dip angle is a complex question

current research on this aspect is relatively less

especially under the condition of facing-slope. Therefore

the article established a new model that considering longitudinal gradient of shield tunneling through introducing the longitudinal slope angle ? on the basis of the trapezoidal wedge model

and deduced the calculation formula of the limit support force of excavation face in this case. Through the data analysis of the calculated value of the support pressure of excavation surface

the article founds that the value of angle ? only affect much more by angle ?

the effects of the soil cohesion c

soil density ?

tunnel diameter D

depth of shield H and additional pressure of earth’s surface q on the value of angle α is less. Under the condition of c is considered

the value of angle ? will decrease gradually with the value of c increases

and the value of angle ? will only change small around a constant value when the value of c

φ and D is fixed. Meanwhile

the value of angle ? will increase gradually as the value of D increases. We can take no account of ?

q and H when calculate the value of angle ? for it’s less effects. Finally

a calculation formula of sliding surface dipping angle is obtained based on the regular pattern

so as to simplify the solving process.