# Comparative study for evaluating the gradient of the failure function of wells drilled on salt rocks

## Palavras-chave:

Gradient of the failure function, FORM, salt rocks## Resumo

This paper presents a comparative study of strategies for obtaining the gradient of the failure function

used in the First Order Reliability Method (FORM) applied to oil wells drilled on salt rocks. The evaluation

of the mechanical behavior of complex structures is commonly performed using the finite element method. In

these cases, several challenges are found when it is desired to carry out a structural reliability analysis, since the

function that defines the structural behavior is numeric and each query requires running a finite element analysis.

This demands a high computational cost, making it practically impossible to perform the reliability analysis from

classical simulation methods. On the other hand, to use transformation methods it is necessary to evaluate the

gradient of the failure function, which is also a numerical expression, requiring the use of alternative techniques

to perform its calculation efficiently. In this context, this work presents the comparison between several numerical

methods to obtain this gradient. Several methodologies such as the response surface method (RSM), the adaptive

response surface method (ARSM) and the finite differences method (FDM) are applied to a model of an oil well

drilled on salt rocks. The main contribution of this paper is to check the efficiency of some procedures for obtaining

the gradient of the failure function in the evaluation of the structural behavior of oil wells drilled on salt zones.