Identifying dominant failure sequences and key elements in progressive collapse analysis

Abstract

Progressive or disproportionate collapse is characterized by collapse of a structure triggered by failure of a relatively small part of it. Identification and strengthening of weak elements, and mitigation of element failure sequences that may lead to progressive collapse should account for uncertainties and incorporate system level performance criteria and initial damaged states. A reliability-based methodology of assessing threat-independent progressive collapse is developed in this paper.

Given a structure, apart from its intact state, a surrogate structure corresponding to each of its initial damaged states is defined. A ﾑhistoryﾒ of the structure is defined as an ordered set of failed elements up to a given time. Not all histories will lead to system failure; mutually exclusive minimal cut sets consisting of ordered element failure histories (including simultaneous failure of two or more elements) are identified and only the statistically significant ones are followed up to system failure.

The framework is applied to two steel truss structures. Load and member capacities are simulated randomly using Latin Hypercube sampling. Material nonlinearity, geometric nonlinearity and transient dynamic effects due to sudden removal of an element are considered.

Dominant failure sequences, i.e., the ones that contribute most to system failure probability are identified. Moreover, it is found that certain elements having a very low probability of failure in the intact structure, if somehow removed (thus the significance of the surrogate structures), lead to progressive collapse up to system failure. Failure sequences starting with these elements do not have a high contribution to overall system failure probability, but are important contenders for the ﾑkey elementﾒ, which may need to be strengthened.

Both for the intact and surrogate structures, most of the failure probability is contributed by only a few minimal cut sets. Ordering of element failures is crucial in defining the cut sets, since several ordered sequences exhibit asymmetry. Ignoring dynamic effects changes failure probability estimates but not dominant failure sequences. Neglecting nonlinearities, however, affects the failure probabilities of the sequences and may change or eliminate key elements.

The outlined framework eliminates the need to consider bounds on the system failure probability since the ordering makes the minimal cut sets mutually exclusive and thus statistically independent. The results suggest that strengthening only the least reliable elements of the intact structure, without accounting for failure progression in surrogate structures, may not be sufficient to mitigate progressive collapse.