Textos de lectura

φcr is the concrete creep coefficient; ν is the Poisson ratio for concrete; and fct

is the tensile strength of the concrete. In the final phase of chloride-induced corrosion, the time (years) from the first instance of cracking to the maximum allowable cracking is (Vu and Stewart 2005):

Tcp = 0.0167i−1.1corr " 42.9 _wc C −0.54 + _w lim− 0.3 0.0062 1.5# (2.29) Where wc is the water/cement ration; and wlimis the maximum crack size. The

ability to be able to determine the time in which the structure is expected to develop critical cracking enables a more accurate estimation of the future reli- ability of the structure. In addition to modelling this critical crack propagation, it is also possible to account for the expected loss of an effective area in a time- dependent reliability model. Two models for reinforcement section loss are often considered: uniform corrosion and pitting corrosion, for which numerous methodologies exist for the calculation of section loss (Andrade et al. 1993, Val and Melchers 1997). As section loss increases, the structural capacity of criti- cal structural elements is compromised and thus the reliability of the structure is also compromised. This section loss can be modelled using the stochastic methods mentioned previously. The application of these methods will be seen in Chapter 4, whereby single point in time estimations of section loss be will evaluated and used to compute reliability indices at these times. While this rep- resents only one method of computed time dependent reliability, it is adequate to reach the objectives of this thesis.

2.7

Conclusion

In this chapter, a performance-based approach to the design and assessment of structures was presented through the implementation of the probabilistic reliability method. The basis of the method was explained and shown to be present in modern structural design codes of practice. The rationale behind the use of this method is how it allows the stochastic modelling of variables in the limit-state design, which is more reflective of actual structural realization than the standard deterministic approach. The various reliability methods used to compute the safety classification of structures were shown, and guidance was given on which method should be chosen in response to the requirement of the structure.

The modelling of the basic variables for load and resistance was presented, and the sensitivity of the method to input parameters was highlighted, along with the potential advantageous by-products of using the method; such as paramet- ric sensitivity and parameter importance measures. The practical hindrances to the widespread adoption of the method have been resolved in the development of software applications and the continued efforts to improve the robustness of the method. In Chapters 3 and 4, the effect that disparate information levels for load and resistance modelling have on β will be shown.

Chapter 3

Reliability Analysis with Uncertain

Parameters

3.1

Introduction

3.1.1

Overview

In the previous chapter, a background has been presented to the structural relia- bility method, from which it can be seen the role that small changes on the basic input model can have on the computed reliability of the structure. With regard to our basic model formulation of Equation 1.1, this chapter will investigate the uncertainty in information surrounding the resource variable R. By increasing the uncertainty in the basic variables, the level at which reliability analysis is compromised to a point that it becomes difficult to extract any valuable infor- mation from the analysis can be estimated. From the analysis, it can be seen that it is possible to identify the most important parameters that influence the reliability index of a particular bridge type; however, these calibrations become clouded when more uncertainty in information is introduced to the model. Presented here is a reliability analysis of three bridges; comprising reinforced concrete slab, reinforced concrete beam-slab, and prestressed concrete beam construction, with a focus on the sensitivity analysis and the analysis of param- eter importance measures. The basis of the analysis stems from the possibility of investigating similarities in various parameters, leading to the establishment of network-level indicators based on fully probabilistic assessments; as these bridges are typical of construction details on road networks. A probabilistic

analysis is conducted, taking uncertainty in relation to the available informa- tion into account. Parametric importance measures are established across the three bridge types, and patterns identified from these studies suggest the po- tential for reliability-based network calibrations of bridge structures.

3.1.2

Background

As bridge infrastructure networks age, it is often necessary to employ non- deterministic techniques in the assessment of intervention options for deteri- orating network assets to maintain an adequate level of safety throughout the network (Žnidariˇc et al. 2011). Probability concepts have been shown to have significant advantages in the design and assessment of engineering structures, specifically structural reliability methods (Ang and Tang 2007). A reliability- based approach for quantifying the safety of structures enables a lifetime eval- uation of both individual and networks of structures (Akgül and Frangopol 2004a,b, Frangopol and Das 1999, Liu and Frangopol 2006a,b, Frangopol and Liu 2007a,b, Frangopol 2011, Bocchini and Frangopol 2011a,b,c, Saydam et al. 2013). While this method is commonly implemented at both a component and system level for an individual bridge in isolation (O’Connor and Enevoldsen 2008, Estes and Frangopol 2001a), there are advantages to conducting a reli- ability analysis for a network of bridges (Frangopol and Bocchini 2012); high- lighting critical components and providing the stakeholders of bridge stock with comparable safety indices and sensitivity measures (O’Connor and Enevoldsen 2007, Dong et al. 2014).

The effective allocation of capital resources seeks to minimise the inherent risks associated with investments through the use of advanced methods (Mueller and Stewart 2011). Reliability methods are an effective tool for the monitoring of the asset base and, thus, allowing the prioritisation of intervention and invest- ment requirements in a more careful and rational manner. Intervention can be focused to address the most important parameters that govern the safety of the bridges, as highlighted by the parametric sensitivity and parameter importance factors, which are beneficial by-products of reliability assessments. Conducting this analysis over a network allows for the comparison of different parameters and uncertainties in each bridge type, and investigates correlations that arise between them (Hanley and Pakrashi 2014). This emphasizes the need for a network based calibration of the importance of certain critical parameters, and