Practical Monte Carlo Based Reliability Analysis and Design Methods for Geotechnical Problems

Reliability analysis is an important tool for quantifying uncertainties in analysis and design of engineering systems. In the past decades, the so-called first-order reliability method (FORM) (Ang & Tang, 1984) was the main stream method for reliability analysis. This method transforms a reliability analysis problem into an approximate optimization problem so that the required computation is minimized. Nonetheless, such transformation comes with some premises and tradeoffs: (a) to make the optimization problem tractable, the number of random variables of the target problem cannot be too many; (b) the problem at hand is better to be lightly nonlinear to avoid large bias in the estimated reliability; and (c) the engineers must have basic skills for solving nonlinear optimization problems. The first two premises may be questionable for realistic geotechnical problems because there are typically numerous random variables in realistic geotechnical engineering analyses and designs. Although techniques are developed to reduce the number of random variables (e.g., Ghanem & Spanos, 1991), their generality and accuracy are not yet proved. Therefore, for realistic geotechnical engineering analyses and designs, FORM may not be the best solution. More seriously, average engineers may not have the knowledge and skills for nonlinear optimization. It is not trivial for them to implement FORM, even for the simplest geotechnical design examples. Given the rapid growth of nowadays personal computers (PCs), massive computations are now more possible than ever. In particular, Monte Carlo simulations (MCS) can nowadays be implemented for the purpose of reliability analyses even with PCs. MCS is general for the number of random variables and the problem complexity; hence the limitation of FORM can be easily overcome. Moreover, the basic idea of MCS is very simple and intuitive. Finally, geotechnical models can be treated as black boxes when implementing MCS. All these features make MCS attractive for practicality. The only criticism for MCS is that it is inefficient for problems with very small failure probabilities (or with very high reliabilities). However, this limitation has been gradually removed by the recent advancements in the Monte Carlo based reliability methods. The goal of this chapter is to demonstrate the uses of some Monte Carlo based reliability methods and reliability-based design methods. In particular, a realistic geotechnical design example is developed for the purpose of demonstration: the implementation of all methods