Based on the upper bound theorem of limit analysis

the stability of the three-dimensional reinforcement slopes was investigated by using the pseudo-static analysis method under the horizontal and vertical seismic forces. Both uniform reinforcement and triangular reinforcement patterns were considered

and analytical expression was derived to calculate the required critical reinforcement strength to prevent the failure of reinforced slopes. The validity of this method was verified by comparing with the results of existing literature

and the effects of the ratio of slope width to height and horizontal and vertical seismic force coefficients on the stability of three-dimensional reinforced slopes were discussed. The results show that with the increase of the ratio of slope width to height

the critical reinforcement strength of the slopes increases under seismic forces

but the changing rate gradually decreases. When the ratio of slope width to height is larger than 10

the critical reinforcement strength of the 3D slopes is similar to that of the 2D cases. With the increase of horizontal seismic force

the critical reinforcement strength of 3D slopes increases nonlinearly. While

with the increase of vertical seismic force

the value of the critical reinforcement strength increases approximately linearly. In addition

with the increase of slope angle

the effect of vertical seismic force on the critical reinforcement strength becomes more significant. The changing rule of the critical reinforcement strength under two reinforcement modes is consistent. Moreover

the stability values of triangular reinforcement mode is always smaller than that of uniform reinforcement mode

and is more conducive to maintaining the stability of the slopes. Finally

some engineering suggestions are proposed for practical projects.