# Probabilistic Numerical Models using Monte Carlo and Point Estimate Methods

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OnePetro

Abstract

Probabilistic wedge stability analyses of a cavern are carried out considering two sets of joints J1 and J2 as random parameters with uncertain dip direction and strength parameters. Probabilistic numerical models are constructed employing Monte Carlo and four different point estimate methods.

It is represented that due to the variability of the dip directions of the two joint sets J1 and J2, two failure modes are possible to take place comprising sliding on J1 and J2 as well as sliding on J1 only. The investigations reveal that with respect to the calculation of probability of failure, there is a good agreement among all methods but in respect of failure mode, some point estimate methods could never find the failure mode which corresponds to sliding on J1 only while some models are able to find this mode of failure if number of realization points or number of random variables are increased.

1 Introduction

When stability of a geotechnical structure is investigated, uncertainties can be taken into account by means of a probabilistic model that in which a probabilistic tool is employed. Since there are various probabilistic methods, different probabilistic models could be created. Nowadays, Monte Carlo Simulation (MCS) as become very popular in geotechnical engineering because it can be used easily without needing to do complicated statistical calculations; as a result, some commercial geotechnical tools were equipped to MCS in order to make probabilistic models (Rocscience Inc. 2015). An important issue that is associated with MCS (Rubinstein & Kroese 2008), is this that when model computation is time consuming, it would be infeasible because small number of simulations leads to inaccurate results and on the other hand large number of simulation leads to inefficiency. Under such circumstances, point estimate method (PEM) (Rosenblueth 1975) is more applicable as it needs smaller amount of computations.

Some workers on reliability such as (Zhou & Nowak 1988), (Harr 1989) and (Hong 1998) have commented on Rosenblueth’s PEM in order to make some improvements. In previous studies (Ahmadabadi & Poisel 2014a, 2014b, 2014c), authors presented an intensive comparison among aforesaid PEMs and other probabilistic methods including MCS, First-order reliability method (FORM) (Hasofer & Lind 1974) and second-order reliability method (SORM) (Breitung & Hohenbichler 1989) utilizing illustrative examples of rock slope. Also, issues of Harr’s and Hong’s PEMs in respect of correlated non-normally distributed random parameters was addressed through the NATAF transformation (M.A. 1962). At the present study, abovementioned PEMs and MCS are compared with the help of an example of a cavern highlighting another shortcoming of probabilistic numerical models which employed PEMs.

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ISRM-EUROCK-2015-164

October, 2015

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