Probabilistic optimization of welded joints maintenance versus fatigue and fracture Mladen Lukic Â, Christian Cremona * Laboratoire Central des Ponts et Chausse Âes, Bridge Division, 58 Boulevard Lefebvre, F-75732 Paris Cedex 15, France Received 26 April 2000; accepted 12 February 2001 Abstract This paper presents a probabilistic maintenance optimization procedure for welded joints damaged by fatigue. The linear elastic fracture mechanics stands as a basis for fatigue crack growth while the crack depth at failure is determined according to brittle or ductile fracture. The ®rst order reliability method being applied, the assessment is then based on reliability indices. At an inspection instant, different events can occur: no crack detection, crack detection, and repair. All these events are uncertain and are expressed in terms of probabilities. As they are cost-dependent, the total expected cost of maintenance could be obtained. The inspection instant is therefore searched by minimizing that total expected cost. Such an approach appears as a good compromise between reliability and costs. The paper provides some sensitivity studies and an application on a real case. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fatigue; Fracture; Welded joints; Highway bridges; Inspections; Repairs 1. Introduction Welding induces some defects which help small cracks to appear. They are often localized at the weld where they can grow under loading and can lead to the joint failure. The conditions governing crack growth are respectively struc- tural geometry, initiation site, material characteristics and loadings [1]. In general, all these conditions are random. Therefore, an appropriate analysis of fatigue phenomena consists by treating the problem in a probabilistic manner. Furthermore, the design of some types of bridges in France Ð for instance, two girder composite bridges Ð allows very low degrees of redundancy. The stock of composite bridges constructed according to that design is relatively young and consequently few defects and cracks have been yet detected. For achieving such a design, high performance material and construction quality are usually required. Nevertheless, maintenance constitutes a comple- mentary and necessary approach to design in order to reduce risk of failure. Therefore, the question arises to know and to assess the reliability of a component as far as a crack is detected. Consequently, inspections have to be chosen in such a way that risk of failure is controlled. But, maintenance actions are also cost-dependent and a rational maintenance must therefore rely on a balanced compromise between cost and risk. In order to rationalize maintenance actions, management systems have been developed, helping to a standardization of the procedures through the development of inspection manuals and the implementation of databases. Experience acquired with these procedures leads today to de®ne other approaches in which rationality is based on the optimization of maintenance costs. This optimization requires methods that take into account technical, econom- ical, management points of view as well as theoretical or practical aspects. Offshore engineering has already success- fully rationalized its maintenance actions by using risk- based inspection procedures and numerous papers have been published on that subject through the ICOSSAR and OMAE conferences see for instance, [9,10,11], the latter giving a general view about risk-based inspection in offshore engineering). It is nevertheless only recently that the corresponding steps have been undertaken for bridges [13,16]. The present paper goes a few steps beyond the current state of tools and its main purpose is to introduce a risk-based inspection procedure for optimizing the most suitable inspection instant in welded joints maintenance. An application on a real bridge is given. This approach is today part of the researches carried out in a french National Research Project MIKTI project) dedicated to the develop- ment of new composite bridges. One of the objectives of Reliability Engineering and System Safety 72 2001) 253±264 0951-8320/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S0951-832001)00019-9 www.elsevier.com/locate/ress * Corresponding author. Tel.: 133-1-4043-5344; fax: 133-1-4043-6515. E-mail address: christian.cremona@lcpc.fr C. Cremona).