Numerical Stability Analysis of Undercut Slopes Evaluated by Response Surface Methodology

One of the most important tasks in designing the undercut slopes is to determine the maximum stable undercut span to which various parameters such as the shear strength of the soil and the geometrical properties of the slope are related. Based on the arching phenomenon, by undercutting a slope, the weight load of the slope is transferred to the adjacent parts, leading to an increase in the stability of the slope. However, it may also lead to a ploughing failure on the adjacent parts. The application of counterweight on the adjacent parts of an undercut slope is a useful technique to prevent the ploughing failure. In other words, the slopes become stronger as an additional weight is put to the legs; hence, the excavated area can be increased to a wider span before the failure of the slope. This technique could be applied in order to stabilize the temporary slopes. In this work, determination of the maximum width of an undercut span is evaluated under both the static and pseudo-static conditions using numerical analyses. A series of tests are conducted with 120 numerical models using various values for the slope angles, the pseudo-static seismic loads, and the counterweight widths. The numerical results obtained are examined with a statistical method using the response surface methodology. An analysis of variance is carried out in order to investigate the influence of each input variable on the response parameter, and a new equation is derived for computation of the maximum stable undercut span in terms of the input parameters.