Three-dimensional calculation method for stability against overturning of overhanging rock based on limit equilibrium method

In the field of overhanging rock prevention and control, the stability calculations have traditionally used simplified two-dimensional profiles as the calculation model. However, the irregular shape of overhanging rocks in nature cannot be accurately represented by this simplified model, leading to limitations in stress analysis. To address this, a three-dimensional calculation method for overhanging rock stability was developed based on limit equilibrium theory and previous research. The proposed method focuses on the stability against overturning of overhanging rocks controlled by the tensile strength of the trailing edge crack. A three-dimensional calculation formula was derived, taking into account the tension resistance, water pressure, and moment of the trailing edge rock. The formula was implemented using numerical integration and spatial geometry methods, providing a comprehensive approach to analyzing the stability of overhanging rock. To validate the proposed method, an application was conducted using the Diaozui overhanging rock in the Qutangxia area of the Three Gorges Reservoir. Numerical analysis was performed to verify the results. By analyzing the stability of different forms of overhanging rock in three dimensions, the relationship between the three-dimensional stability calculation results and the traditional two-dimensional stability analysis was explored. The findings revealed that the shape of overhanging rock significantly impacts the stability calculation results. It was concluded that three-dimensional calculations provide more accurate and practical results compared to the traditional two-dimensional approach.