A new approach to grid search method in slope stability analysis using Box-Behnken statistical design

- Prediction model for safety factor is developed using statistical design.
- Explicit equations for locating the slip center grid are proposed.
- Impact of geometrical and soil parameters on slope stability is thoroughly evaluated.

Grid search method for locating the critical failure surface is extended by deriving additional analytical expressions for slip center grid (xmin, zmin; xmax, zmax), where global minimum of safety factor occurs, including the prediction of minimum and maximum values for safety factor (Fsmin,max) and for slip circle radius (Rmin,max). Derived models are proposed in a form of nonlinear functions of geometrical parameters (slope height H, depth to bedrock d and slope angle β) and soil factors (bulk density γ, cohesion c, angle of internal friction φ and pore water pressure coefficient ru). Research was performed using Box-Behnken experimental design, for which the input data were provided by Spencer limit equilibrium analyzes of different slopes with circular slip surface. Reasonable predictive power of the proposed models was verified both by internal and external validation, latter of which included the analyzes of slopes with random geometrical and soil properties. Regarding the impact of input parameters, β has the strongest influence on response values (Fs, R, x, z), with the predominant linear and quadratic effect. As for the influence of remaining factors, c and φ also have strong impact on Fs, while H and φ have significant influence on slip circle radius and the location of slip center grid. However, due to existence of two-factor interactions, it is shown that the effect of β on Fs, x, z and R is highly dependent on the values of c, φ, ru, H and d/H, including the significant effect of ru × φ, c × H and c × γ. When compared to traditional grid search method, proposed approach could be used to locate the circular slip surface with global minimum of safety factor, without the need for additional slope stability analyzes.