Safety Factor on Rock Slopes with Tensile Cracks Using Numerical and Limit Equilibrium Models
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ORIGINAL PAPER
Safety Factor on Rock Slopes with Tensile Cracks Using Numerical and Limit Equilibrium Models Norly Belandria
. Roberto U´car . Alfredo Corredor . Ferri Hassani
Received: 30 June 2020 / Accepted: 28 October 2020 Ó Springer Nature Switzerland AG 2020
Abstract Through the research it describes an analytic methodology, which allows to determine the minimum safety factor depending on the depth of tensile crack and the inclination of surface failure on the most critical condition, considering at the same time, surcharge, seismic effect and water pressure. Therefore, it studies the stability of rock slopes considering that the potential of failure surface it is constituted by two blocks with different inclinations. The superior block is limited by a tensile crack that is represented by a fracture without displacement. On the other hand, on the inferior block, geometry is formed by a potential slide plane of a inclination with the horizontal axis, in which are acting shear stresses. Fracture on superior block is characterized by a normal-tensile stresses field that act over the crack whose presence originates when the rock loses its original cohesion. Finally, comparisons are made through examples with the limit equilibrium method and finite elements method, where it determines the safety factor on dry state, water and seism, being all of them too similar. Besides, the methodology compares the track depth and the distance between the ´ car A. Corredor N. Belandria (&) R. U Geological Engineering School, University of Los Andes, Me´rida, Venezuela e-mail: [email protected] F. Hassani Department of Mining and Material Engineering, McGill University, Montreal, Canada
intersection point of tensile crack and the edge of the slope face, results shows that the analytic methodology is very conservative and throws the less values of this distances. Keywords Tensile crack Safety factor Superior and inferior blocks Rock slopes Finite element method Limit equilibrium method
1 Introduction A significant number of investigations on classical limit equilibrium method (LEM) is usually used to evaluate stability with tensile cracks in slopes (Fellenius 1936; Terzaghi 1943; Bishop 1955; Morgenstern and Price 1965; Spencer 1967, 1968; Sarma 1973). Therefore, in the classical LEM, the cracks are usually preset vertically at the upper slope surface (Hoek and Bray 1977). On the other hand, the failure surface analize on soils and rock slopes consist to divide it on two failure planes (Hoek and Bray 1981; Hoek and Brown 1980, 1988, 1989, 1997; Hoek et al. 2002; Priest 2005; Pariseau 2007). However, the cracks may arise at the trailing edge of slope caused by the sliding body (Dai et al. 2008; Taghavi et al. 2010; Zhang et al. 2012; Utili 2013), and cracks may open up as part of the collapse mechanism (Michalowski 2013; Abd and Utili 2017), but may also be deepened by seismic
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Geotech Geol Eng
activity (Zhao et al. 2016), water and surcharge (Shukla et al. 20
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