Abstract: Compared with the existing method combining soil arch shape and horizontal layer analysis, this study has no assumption of soil arch shape and shear stress is considered. The stress solution of any point in the sliding soil is obtained by solving equilibrium differential equations of the two-dimensional differential element, and the active earth pressure imposed on the rigid wall is further derived. Subsequently, based on the stress state of any point in the sliding soil, the analytic expression of the arch shape is established. Furthermore, the effects of internal friction angle, soil-wall friction angle on earth pressure and soil arching shape are discussed. Finally, the obtained results are compared with the results derived from existing theory and experimental results, and the conversion formula between the proposed active earth pressure coefficient and Coulomb theory is obtained. The results indicate that the proposed distribution of earth pressure is in good agreement with the experimental results, especially in the case of high wall. When the soil-wall friction angle is small, the calculated soil arch is similar to the arc, and the soil arch becomes steeper in terms of the increase of soil-wall friction angle, which is always under the parabolic arch. The practical formula is only related to , which is convenient to use in engineering.

Key words: active earth pressure, soil arching effects, two-dimensional differential element, stress analysis, sandy soil