| The spatial shape of the 3D passive slip surface behind the retaining wall is difficult to determine,and the determination of the 3D passive slip surface is of great significance for the study of 3D passive earth pressure.First,the FLAC3D software is used to establish a numerical model of the retaining wall with a limited width-to-depth ratio and behind the retaining wall with non-cohesive soil.The regularity of the soil slip surface on the inside and end of the retaining wall is analyzed under different parameters such as the width-to-depth ratio of the retaining wall,the different internal friction angles of soil mass and the different friction angle ratios of the wall-soil contact surfaces.Then,based on the numerical simulation,the thin plate smooth spline function is used to search the 3D soil slip surface at the end of the retaining wall,and the 3D passive soil slip surface equation is fitted and summarized.Based on the determi nation of the slip surface,the 3D passive earth pressure and the resultant action point of the earth pressure of the retaining wall are deduced and calculated through mechanical analysis.The following research results were obtained:The numerical simulation shows that the section of the slip surface on the inside and the end of the retaining wall is basically unchanged with the change of the width-to-depth ratio of the retaining wall.The longest distance between the end and the inner slip surface of retaining wall along the X-axis under different soil internal friction angles is basically the same as that of Rankine slip surface.When the friction angle ratio of the wall-soil contact surface isδ/?=0,the inside sliding body of the retaining wall width can be regarded as a wedge.Because the slip surface at the end of the retaining wall is not easy to determine,based on numerical simulation,the width-to-depth ratio of the retaining wall b/h=2,the friction angle ratio of the wall-soil contact surfaceδ/?=0,and the thin plate smooth spline function is used to search 3D slip surface at the end of retaining wall under different internal friction angles of soil mass.By analogy to the failure of foundation bearing capacity,the 3D sliding surface at the end of the retaining wall under different friction angles is fitted with a function equation,and the 3D sliding surface equation at the end of the retaining wall is summarized.Under the conditions of rigid retaining wall translation mode,vertical back wall,horizontal and non-cohesive soil,andδ/?=0,the 3D slip surface is determined based on the 3D slip surface equation at the end of the retaining wall.The volume of the 3D slip body under different width-to-depth ratios and different internal friction angles of soil mass can be obtained.and three-dimensional passive earth pressure calculation method is derived through mechanical analysis,and the method is verified and analyzed.The analysis results show that:（1）Compared with the Soubra passive earth pressure coefficient,the three-dimensional earth pressure coefficient obtained by the calculation method in this paper is closer to the passive earth pressure coefficient of numerical simulation.（2）With the increase of the width-to-depth ratio of the retaining wall and the decrease of the internal friction angles of soil mass,the 3D calculated passive earth pressure coefficient tends to Rankine passive earth pressure coefficient.When the width-to-depth ratio of the retaining wall is less than 4,the 3D calculated passive earth pressure coeffi cient and Rankine passive earth pressure coefficient are obviously different.（3）In the translation mode,the position of the resultant action point of 3D passive earth pressure is slightly lower than that of Rankine passive earth pressure.With the increase of the width-to-depth ratio of the retaining wall and the decrease of the internal friction angles of soil mass,the position of the resultant action point of 3D passive earth pressure tends to that of Rankine passive earth pressure. |
