Research on Tension Cracks and Active Earth Pressures in Cohesive Backfills of Retaining Walls

The Rankine theory is restricted to calculating earth pressure on the vertical and smooth back of retaining walls, as well as the horizontal backfill surface. Hence, it is of great significance to research the active earth pressure of cohesive fill in scenarios involving a rough oblique wall back and a nonhorizontal filling surface. The sliding soil mass behind the wall is divided into two parts: elastic zone and plastic zone. Based on the upper-bound theory of limit analysis, an energy conservation equation was established in this paper, deriving analytical formulas for the depth of tensile cracks in cohesive soil and the inclination angle of the slip surface. The analyzed failure plane inclination angle was applied to the thin-layer element method, deriving the expression for active earth pressure by establishing force balance equations and a moment balance equation, which can be degenerated into a Rankine solution. Compared with relevant theories, the proposed theoretical solution in this paper better matches the experimental values, verifying the effectiveness of the proposed formulas. Moreover, the influence of soil cohesion, internal friction angle, wall–soil friction angle, wall–soil adhesion, wall back batter angle, and backfill surface slope angle on crack depth and active soil pressure was explored.