Reliability-based life cycle assessment for civil engineering structures

Schnetg R., Klinzmann C., Hosser D.

Abstract:
A modern lifetime oriented design of structures includes inspection and monitoring strategies. Structural health monitoring guarantees that the load bearing capacity, the serviceability and the durability of the structure remains ensured. One main focus of the collaborative research center (CRC) "Life cycle assessment of structures via innovative monitoring", funded by the DFG at Braunschweig University of Technology, is to optimize methods of structural health monitoring. In this article the framework for reliability-based system assessment developed by project field A1 of the CRC is described. The framework can be used to identify critical weak points or failure paths of a structure. It bases on methods of system and reliability theory. The gained knowledge about the structural system is used to formulate a probabilistic model with a fault tree, limit-state equations and information about the random variables for the structure. Using the results of the reliability analysis, further decisions concerning an inspection and monitoring design can be made. For the illustration of the framework a bridge example is used. The main focus in the article lies on the ultimate limit states for the flexure and fatigue failure of the bridge structure. The structure is a multi-span plate-girder bridge over two fields with two girders and a span width of 25 m for each field. The bridge is pre-stressed with post-tensioning tendons. The assessment starts with a survey of possible weak points. First information about weak points of structures can be extracted from analyses of past damages. These analyses are the basis to determine failure scenarios. Further information about possible weak points and failure scenarios can be derived from the structural design process. In the example, the weak point analysis is based on the structural design. The structural design for the bridge structure shows high action-effects in the cross sections at midspan and at the support. After a failure of the cross section in one of these areas, the structure does not yet fail. A plastic hinge arises and a redistribution of the applied load is possible. This means that the collapse of the structure depends on the failure of more than one component. All failure paths of a structure will be identified on the basis of an event-tree analysis which is an element of the framework. In the event tree, which is shown in the article, the failure in point 1 represents a cross-sectional failure at midspan of the first bridge field. The failure in point 2 represents a cross-sectional failure at the support and the failure in point 3 represents a cross-sectional failure in the second bridge field. A system collapse would occur after a formation of two plastic hinges. For the reliability analysis the event tree will be transformed into a fault tree. Therefore, a schematization for the design of the fault trees was developed (Klinzmann et al. 2005). In the first step, a relation between the structure and the abstract elements in the fault tree is established. This is done with the so-called "failure points". A failure point of a structure can be any weak point of the structure where a failure can occur, e.g. the points 1-3 in the bridge example. The type of failure occurring at a failure point is called "failure mode". The failure mode combines the different causes for a failure. In point 1-3 a failure can occur due to flexure failure or due to fatigue failure. A failure path normally consists of more than one failure mode, which needs to occur for the system to collapse. All failure modes in a failure path are linked in parallel systems. Per definition, the failures have to occur at different failure points. All failure mechanisms of a structure are linked, using a serial system, because they are all single reasons for system failure. In case that a failure (Graph Presented) mode already would lead to a failure of the system, this failure mode is as well a failure mechanism. The limit state functions are modeled in the next step of the setup of the probabilistic model. The limit states in the example are formulated using analytical models. The flexure capacity of the cross section can be calculated from the equation of the equilibrium of internal forces. Apart from the flexure capacity, also the limit state for fatigue failure of the tendons is to be analyzed. The describing model for fatigue failure is based on the Palmgren-Miner-hypothesis. The first reliability analysis contains a prognosis based on the initial stochastic model and an assumed deterioration. The prognosis of the reliability is carried out for the next five years (Fig. 1). A further result of the reliability analysis is the influence of components on the system reliability, the so-called sensitivity of components. In this bridge structure the fatigue failure at midspan of both fields have a predominant influence on the system reliability. Based on these results a continuous monitoring of the action-effects due to loading is reasonable. The adaptation of the first prognosis on the current state of the bridge should be carried out after three years because there is a sufficient safety margin between the prognosis and the target reliability of structural codes (e.g. β = 4.7 from Eurocode). For this purpose a monitoring of the pre-stressed tendons is recommended. The dotted line in Figure 1 shows a possible development of the reliability with consideration of the monitoring results. This procedure is part of the developed structural evaluation and assessment process (Schnetgo¨ke et al. 2005). The article provides an overview of the framework of reliability-based life cycle assessment, which was developed to optimize the structural health monitoring process. Further, the framework gives support to civil engineers when they have to plan monitoring measures. Further research will focus on the modeling of systems and the extension of the usage of results from the monitoring in the assessment process of structures. Especially the consideration of deterioration models within the probabilistic model is of great significance.

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