Active earth pressure calculation method for gravity retaining wall of railway subgrade based on discretized potential sliding surface inclination angle

The cross-section of the backfill behind railway subgrade gravity retaining walls is trapezoidal, and the backfill is subjected to train loads. General formulas of Coulomb earth pressure theory are not applicable for the determination of the location of dangerous sliding surface and the magnitude of active earth pressure under such complex engineering conditions, making it difficult to perform stability analysis for gravity retaining walls. This paper firstly proposes a method for determining dangerous sliding surfaces based on the limit equilibrium of sliding soil, and calculates the active earth pressure resultant force. According to the principles of equivalent resultant force and equivalent total moment, the force arms of the horizontal and vertical components of active earth pressure are determined. Subsequently, stability analysis of railway subgrade gravity retaining walls considering two failure modes of sliding and overturning is performed. Results show that the proposed method achieves high accuracy with simple calculation principle, less calculation demanding and fewer calculation constraints, and it is recommended to have a step size of for the inclination angle change of the sliding surface to ensure high accuracy and efficiency simultaneously. Furthermore, this paper analyzes the impact of parameters e.g., the distribution of the over load, the width of the overload, the inclination angel of the wall back and the angle of the inner slope and summarizes the influence patterns of these parameters on the magnitude of active earth pressure, the position of active earth pressure, and the safety of different failure modes.