Page - 977 - in Book of Full Papers - Symposium Hydro Engineering

cost. Any method in design satisfying both aspects is very precious. These methods are identified as techniques for determining the reliability of system. Today, it is common to express reliability in the form of a reliability index, which can be related to a probability of failure. The reliability index β provides a more meaningful measure of stability than the FOS. Geotechnical engineers have long recognized that FOS has little physical meaning and that the choice of a satisfactory value is fraught with difficulty. Conversely, the reliability index describes safety by a number of standard deviations (i.e. the amount of uncertainty in the calculated value of FOS) separating the best estimate of FOS from its defined failure value, that is to say 1.0. It is a more explicit approach. β is the number of standard deviations by which the expected value of the factor of safety is away from the unsatisfactory performance condition, or the factor of safety equaling one. Obviously larger reliability index indicates the higher confidence of slope safety [11,12]. The reliability index can be computed by Eq. 3. 𝛽 = 𝑚 𝐹 𝑂 𝑆 −𝐿 𝜎 𝐹 𝑂 𝑆 [3] where mFOS is the mean factor of safety, L is a limit state value usually equal to 1 and σFOS is the standard deviation of the factor of safety [13]. To determine the reliability index β, Monte Carlo simulation can be employed. Monte Carlo simulation is a method for iteratively evaluating both stochastic and deterministic systems using randomly generated points to cover the range of values that enter into a calculation. It is just one of many methods for analyzing uncertainty propagation where the goal is to determine how random variation, lack of knowledge, or error affects the sensitivity, performance, or reliability of the system being modelled. To perform such a study, the data analyst generates a random value represented by a probability density function, for each uncertain variable and performs the calculations necessary to yield a solution for that set of values. This gives one sample of the process. The trials are repeated many times, giving many samples of the process. Once a large number of runs have been completed, it is possible to study the output statistically and to obtain values of means, variances, probabilities of various percentiles, and other statistical parameters. Considering safety factor, repeating process continues until a distribution of factors of safety sufficient to define the probability of failure. Regarding to this, the probability of failure and reliability index is calculated [11,14]. 5. ANALYSIS Employing Monte Carlo simulation, a Python code is developed to evaluate the vegetation effect on slope stability. Discrete values of each variable interacting with slope stability are randomly selected from its probability distribution. Those distributions are depicted in Fig. 1 and 2. Using a set of such discrete values, a value of the performance function FOS is then obtained. This process is repeated 977