Method to calculate active earth pressure considering soil arching effect under nonlimit state of clay

By taking the limited range of clay behind the retaining wall as the research object, considering soil arching effect under non-limit state, and adopting the angle of the fracture surface obtained by the plastic upper limit theory and the variation law of lateral earth pressure coefficient obtained by hypothesis of multiple slip surfaces, an analytical formula for the active earth pressure of finite soil is derived. The expression can also be reduced to the formula for the active earth pressure with half-infinite width. Compared with that of the model test, the proposed theoretical solution is in preferably consistency with the experimental value. So the rationality of the analytical solution is proved. Further parameter analysis shows that the angle of the rupture surface increases linearly with the friction angle of the soil. The angle of the rupture surface increases slightly as the aspect ratio of the limited soil $B/H$ decreases. The angle of the rupture surface and the ratio of the outer friction angle of the basement retaining wall to the inner friction angle $\alpha /\phi$ are positively correlated. The angle of the rupture surface and the ratio of the outer friction angle of the foundation pit retaining wall to the inner friction angle $\delta /\phi$ are negatively correlated. When $\alpha /\phi$ is greater than or slightly less than $\delta /\phi$, the angle of the rupture surface increases monotonically with the displacement ratio $\eta$. And when $\alpha /\phi$ is much smaller than $\delta /\phi$, the angle of the rupture surface increases first and then decreases with the increase of $\eta$. The active earth pressure decreases monotonously with the reduction of $B/H$, and its distribution gradually changes from bullet shape to bell shape. The value of active earth pressure is negatively correlated with $\delta /\phi$,$\alpha /\phi$ and $\phi$, and the nonlinearity of active earth pressure curve gradually increases with the increase of $\delta /\phi$ and $\phi$.