The tail-oriented multi-normal model method for partially correlated seismic fragilities in probabilistic risk assessment

Abstract

Many seismic-induced failures are due to shaking effects in response to common ground motions. Since the effects of shaking are propagated to equipment with varying configurations located at the same or different locations, there is often a degree of partial correlation between these failures. Common practice in seismic probabilistic risk assessment (SPRA) of nuclear facilities typically idealizes this partial correlation as either perfect correlation or full independence. Recent studies indicate that refining this practice for structures or components with considerable risk contributions can lead to significant effects on the SPRA outcome. Methods and techniques to incorporate the modelling of partial correlation in SPRA models have received increasing research attention in recent years, and a few recent SPRAs explicitly modelled it for risk-significant contributors. While applicable to single-unit (SU) SPRA, explicit modelling of seismic fragility partial correlation may be even more impactful for multi-unit (MU) SPRA.

Several methods with various degrees of rigor exist in the literature for explicitly modelling partial correlation between seismic fragilities in a probabilistic risk quantification. The available rigorous methods typically involve the use of numerical simulation or computationally intensive numerical analysis, which are not practical for inclusion in SPRA qualification. This article discusses the tail-oriented multi-normal model (TMM) method, a robust technique for explicitly modelling partial correlation between seismic fragilities in SPRA applications. The TMM method is based on the Separation of Independent and Common Variables (SICV) concept and is superior to other SICV-based techniques in that it uses an efficient closed-form formulation. This analytical solution is premised on the lognormal probability distribution being a valid representation of seismic-induced failure fragilities, which is commonly accepted in SPRA.

This article is divided into an introduction and four sections. The introduction reviews available relevant literature on the topic, presents relevant technical background elements, and summarizes specific current technical challenges. The first section introduces the TMM method formulation, and implementation steps. The second section presents validation examples. The third section discusses the determination of partial correlation factors and the sensitivity of the TMM method results to the accuracy of the partial correlation factors. The fourth section discusses the use of the TMM method in SPRA models.

The performance of the TMM method is found to be more favourable than the widely used Reed-McCann method both computationally (processing time) and analytically (solution accuracy). The TMM method results are found to be weakly sensitive to fragility analyst judgement in quantifying partial correlation, making it robust against potential bias in such judgements. Furthermore, the TMM method can be readily integrated into SPRA quantification software using two model development alternatives.