A probabilistic multi-scale time dependent model for corroded structural suspension cables

Suspension cable structures, whose constitutive material is mainly steel, suffer from the continuous aggression of the environment (urban, industrial, marine, etc.). These effects appear through corrosion, whose direct consequences are the strong modifications of the geometrical and mechanical characteristics of the components. This induces a notable reduction of the bearing capacity of the cable with time, sometimes resulting in its partial rupture. A large number of broken wires found in the suspension cables of some bridges in France and overseas has largely highlighted the absence of methods for assessing safety levels provided by old suspensions. This paper attempts to solve this problem through a probabilistic multi-scale time dependent model. The cable behaviour can indeed be studied distinguishing the wire scale, the strand scale and the cable scale with a complete decoupling between these scales. Two independent stages are considered: First stage (local description): One determines the constitutive law of an isolated strand section (whose size equals the recovery length), and thus evaluates its response in terms of statistical distributions of the wire's failure. Second stage (integrated description): Explicit laws are deduced from the preceding stage results. It is necessary to integrate, identify and calibrate the constitutive laws as well as their statistical distributions. The cable model can be a composite population, made of a strand's sections with different corrosion evolution rates, because of a more or less aggressive environment. We show that, for a given service load, the theoretical mean lifespan varies between 70 and more than 150 years according to assumptions made on the development of corrosion. This highlights the importance of monitoring, since it can feed into models with additional data. (C) 2005 Elsevier Ltd. All rights reserved.