Thermodynamic theory of the most energy-efficient natural repose angle

This paper describes the formation of the natural repose angle of non-cohesive bulk materials. The repose angle of particulates \(\alpha \) is the angle between the tangent plane to the surface of the slope and the solid base. The paper presents a thermodynamic theory for the formation of the most energy-efficient natural slope \(\alpha \approx \) 30\(^{\circ }\) that can be found very often both in nature and industry. The theoretical foundation is based on Janssen theory of the statistical distribution of vertical and horizontal stress and adds its own consideration about dissipative work during the movement of material as a slope is being formed. The presented model is expanded to include an experimental part describing four methods of creation of a natural repose angle on three sand samples. The experiments performed demonstrated the validity of the submitted theory and the thermodynamic model with certain deviations derived from the essence of the experiments performed. These experiments explain a frequent occurrence of natural slopes with a repose angle of around 30\(^{\circ }\).