Reliability analysis of a rock slope in Sumela monastery, Turkey, based on discrete element and response surface methods

Dadashzadeh, Neda
It is widely recognized that a single factor of safety (FOS) calculated by traditional deterministic analysis methods may not represent slope safety due to involved uncertainties. The First Order Reliability Method (FORM) is one of the extensively used probabilistic methods in slope stability studies to quantify the uncertainties in the parameters. FORM can be easily applied when the slope is analyzed based on limit equilibrium methods. However, the recent numerical techniques are almost substituted by the conventional limit equilibrium approaches due to their high performance of representing the real phenomena. Monte Carlo Simulation (MCS) technique is a widely used probabilistic tool to consider the uncertainties. However, although advanced modeling techniques in slope stability analysis are successfully used in deterministic studies, they have so far found little use in probabilistic analyses due to their high computation cost. Alternatively, FORM can calculate the probability of failure (Pf) in more efficient way rather than MCS method. However, in order to be able to perform reliability studies, the corresponding limit state failure function is essential. It is not possible to generate an explicit failure function in cases simulated by numerical methods. The Response Surface Method (RSM) is usually used to approximate the implicit limit state failure function using an equivalent explicit mathematical function of the random variables. Since the approximated limit state function is explicit, the FORM can be applied to estimate the Pf. In this thesis, a reliability assessment methodology is developed by using three dimensional distinct element code, 3DEC, based on RSM. Once the limit state surface is generated, FORM is performed to calculate the Pf. The methodology is used to calculate the Pf of a selected potential rock wedge in Sumela Monastery, Turkey. The potential wedge is located at height of approximately 200 meters from the toe of the cliff with volume of about ten million m3. Rockfall evidences on the wedge indicate the slope instabilities. The Pf of the wedge is calculated to be 16.3% by 84 simulations in 3DEC based on proposed methodology which is about 10% of the number of simulations required for a MCS. It is concluded that by converging to the limit state surface obtained from RSM, slope instabilities occur inside the model and cause increase in total displacements and vertical velocity. It is also revealed that after about 10 cm of total displacement, the slope represents a critical uncontrollable situation which requires development of risk mitigation strategies.


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Citation Formats
N. Dadashzadeh, “Reliability analysis of a rock slope in Sumela monastery, Turkey, based on discrete element and response surface methods,” M.S. - Master of Science, Middle East Technical University, 2015.