Effect of undercut on the lower bound stability of vertical rock escarpment using finite element and power cone programming

In the present study, the stability of a vertical rock escarpment is determined by considering the influence of undercut. Lower bound finite element limit analysis in association with Power Cone Programming (PCP) is applied to incorporate the failure of rock mass with the help of the Generalized Hoek-Brown yield criterion. The change in stability due to the presence of undercut is expressed in terms of a non-dimensional stability number ( σ ci/ γH). The variations of the magnitude of σ ci/ γH are presented as design charts by considering the different magnitudes of undercut offset ( H/ v u and w u/ v u) from the vertical edge and different magnitudes of Hoek-Brown rock mass strength parameters (Geological Strength Index ( GSI), rock parameter ( m i,), Disturbance factor ( D)). The obtained results indicate that undercut can cause a severe stability problem in rock mass having poor strength. With the help of regression analysis of the computed results, a simplified design equation is proposed for obtaining σ ci/ γH. By performing sensitivity analysis for an undisturbed vertical rock escarpment, we have found that the undercut height ratio ( H/ v u) is the most sensitive parameter followed by GSI, undercut shape ratio ( w u/ v u), and m i. The developed design equation as well as design charts can be useful for practicing engineers to determine the stability of the vertical rock escarpment in the presence of undercut. Failure patterns are also presented to understand type of failure and extent of plastic state during collapse.