Analytical and numerical investigation of the critical height of vertical rock slope

Slope stability analysis has received substantial attention in the scope of rock mechanics and rock engineering for many years. Various methods are available for analysing the stability of the vertical slope. The objective of this paper is to extend the proposed theoretical equation regarding tensile strength (σ_t), Poisson’s ratio (ν) and bulk density to estimate the critical height of rock cliffs. It is well known that the tensile strength of the rock can be calculated from the uniaxial compressive strength (σ_c) and the Hoek-Brown constant (m_i). This paper is focusing on the followings: (i) influence of the Hoek-Brown constant on the critical height of the cliff, and (ii) influence of the rock mass quality (ie. Geological Strength Index - GSI) on the critical height of the cliff. For this purpose, limestone has been considered and some analytical calculation has been performed. Also, a numerical approach with Slide 2D software was implemented to calculate the safety factor for different GSI values (100, 80, 60, 40, and 20). The results proved that the factor of safety depends on Hoek-Brown constants and Poisson ratio. Moreover, for unrealistic height with small amounts of Poisson ratio and Hoek-brown constant, the numerical results showed an unstable state. For vertical slopes with a small GSI (GSI=20), apart from the value of Hoek-Brown constant and Poisson ratio, all heights were determined as unstable.