EXPLICIT METHODS. 4.2.1 Monte Carlo simulation (MCS) The term “Monte Carlo simulation” (MCS) embraces a wide class of computational algorithms which are effectively capable of simulating complex physical and mathematical systems. The simulations are performed by repeated deterministic computation of user- defined transformation models using random values as input (i.e. random values drawn from user-generated sampling distributions). MCS is often used when the model is complex, nonlinear, or involves several uncertain parameters. The number of evaluations/repetitions necessary to establish the probability distributions of the output parameters will depend on the number of input parameters, their probability distributions, the complexity of the propagation model and the accuracy requirements of the output. A simulation can easily involve over 10,000 evaluations of the model. Monte Carlo simulation allows consistent processing of uncertainties in input parameters and models, regardless of the degree of linearity and the complexity of transformation models, and of the magnitude of uncertainties in parameters and models. Other notable advantages of MCS over other techniques include: (a) the possibility of appreciating (to the degree of precision desired by the user and imposed by the quality of input data) the shape of the output variable; (b) the possibility of including complex mathematics (e.g. logical statements) with no extra difficulty; and (c) the possibility to model transformation uncertainty directly and to assess its effect on model outputs (Xxxx 2008). Monte Carlo simulation requires the generation of artificial samples of input random variables from purposely selected distributions. Such process requires sequentially: (a) the assignment of a probability distribution type; (b) the assignment of characteristic distribution parameters; and (c) sampling from the distributions. In addition, computation power needs may be large for complex models. The Monte Carlo simulation technique is implemented in some commercial slope stability analysis packages (e.g. Geo-Studio, 2010). However, when the probability of failure is very small, the number of simulations required to obtain an accurate result directly is so large that, except for very simple (or simplified) problems, it renders the application impractical. In these situations the conditional probability of failure can be determined for various low probability scenarios, and then combined, considering the scenario probabil...
