Based on the distribution of normal stresses over three-dimensional (3D) slip surface

a method satisfying four equilibrium conditions is proposed to calculate reinforcing forces of 3D sliding mass for any shape of slip surfaces. A hypothetical model of forces among slices is established based on the classical soil pressure theory analogy and Spencer slices method. The distribution functions of normal stresses over the 3D slip surface are calculated under the equilibrium condition of classical slices

involving three undetermined parameters. The reinforcing force coefficient can be calculated by solving a set of linear equations established with three undetermined parameters and one reinforcing force coefficient

according to the main four equilibrium conditions of the sliding mass. This new method features simple computation process and high precision due to satisfaction of four equilibrium conditions. The method has been successfully applied to the design of reinforcing the potential 3D sliding mass on the left abutment of the Yinpan gravity dam on Wujiang river and is valuable to engineering applications.