It is usually difficult to determine the spatial form of three-dimensional passive slip surfaces behind retaining walls. Based on numerical simulation

this paper assumes friction angle ratio of the wall-soil contact surface to be zero (δ/? = 0)

and uses the thin-plate smoothing spline function to search for the three-dimensional slip surface at the end of retaining wall under different internal friction angles of soil mass. By analogy with the failure of foundation bearing capacity

an equation is proposed to curve fit the three-dimensional slip surface

and the equation for three-dimensional slip surface at the end of the retaining wall is summarized. For translational failure mode of rigid retaining walls with upright wall back

horizontal filling level and non-cohesive soil

δ/? = 0

the volume of sliding body behind the wall is calculated based on the three-dimensional slip surface equation. The calculation of three-dimensional passive earth pressure is deduced

and verification is carried out. The results are obtained as follows: (1)Compared with the Soubra passive earth pressure coefficient

the three-dimensional earth pressure coefficient obtained by the proposed method in this paper is closer to the numerical simulation result; (2)There is a significant difference between the three-dimensional passive earth pressure coefficient and Rankine passive earth pressure coefficient when the length-to-depth ratio of the wall is less than 4.0. As the length-to-depth ratio increases and the soil internal friction angle decreases

the three-dimensional passive earth pressure coefficient reduces to the Rankine’ value

and the position of the three-dimensional passive earth pressure resultant action point tends to be the position of the Rankine’s point.