Traditional theory of soil arching effect is based on the assumption of homogeneous stress distribution in loosening zone. However

because of the influence of main stress axes deflection in loosening zone

the stress distribution is inhomogeneous. Based on Terzaghi’s loosening earth pressure theory

three types of major principal stress path are assumed and then a modified analytical solution of loosening earth pressure is presented considering the influence of stress distribution. DEM is also used to compare the model. The results show that when soils arrive ultimate equilibrium state

the distributions of vertical stress and horizontal stress in loosening zone are concave and convex respectively

and lateral earth pressure coefficient equals to passive earth pressure coefficient on the axle of the loosening zone. Difference among different major principal stress paths is less than 10% and these results are all in agreement with DEM numerical results

which confirms the effectiveness of the modified analytical solution. For the convenience of calculation

it is recommended to assume an arc path of major principal stress in the calculation of relevant projects.