Theoretical Analysis of the Active Earth Pressure on Inclined Retaining Walls

The estimation of earth pressure is crucial in the design of retaining structures. The evaluation of vertical retaining walls has been well studied within the framework of the differential flat element method in prior investigations, in which the vertical stress and maximum principal stress are assumed to be uniformly distributed. Inclined retaining walls have been successfully adopted in excavation engineering. Due to the inclination of retaining walls, the maximum principal stress direction rotates approximately parallel to the inclined wall back, which affects the active earth pressure on the walls. This paper provides an analytical solution to evaluate the active earth pressure on inclined retaining walls. A numerical model is first established to analyze the characteristics of the principal stresses and vertical stress distribution of soil behind walls with various inclination angles. An idealized vertical stress field containing two zones is developed, and a hyperbolic function is proposed to illustrate the distribution of vertical stress at various depths. Subsequently, the relationship between the nonuniform characteristics of the vertical stress and normal stress acting on a differential flat element is established based on a circular stress trajectory. The active earth pressure along the inclined wall is then obtained based on the balance of the forces on the differential elements. The predicted data from the proposed analytical solution are compared with the previous experimental, numerical, and theoretical results with excellent agreement, demonstrating the accuracy of the proposed method.

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