Modelling of the long-term behaviour of reinforced and prestressed concrete beams based on extensive experimental research

Since the unfortunate occurrence of several structural failures and excessive deflections of bridges over the past decades, the awareness rose in the structural engineering community to the issue of the serviceability of structures. In 1996, the Koror-Babeldaob bridge in Palau, which was a prestressed segmentally erected box girder built in 1977 with a world-record span of 241 m, suddenly collapsed 3 months after a remedial prestressing. The remedial prestressing was performed because the deflection after 18 years exceeded 1.5 m with an average prestress loss in the tendons of 50%. The excessive deflections followed by a tragic collapse were the consequence of wrong design codes and recommendations in which inaccuracies in the prediction of long-term deflections related to the creep models played a major role. Serviceability failures of concrete structures involving excessive cracking or deflections are not uncommon, even in structures that comply with code requirements. Studies by Bazant and the RILEM Committee TC-MDC show that in most of the bridges investigated by them, deflections have been underestimated and exceed the maximum acceptable deflection of 1/800 of the span. More than half of the 56 investigated segmentally erected box bridges around the world display an excessive deflection. These unexpected excessive deflections impose a severe risk to the structure’s serviceability and safety and can shorten the service life with vast economic consequences. Hence, current design codes and guidelines regarding long-term prediction models and the associated structural analysis methods are not completely satisfactory. In this context events such as the collapse of the Koror-Babeldaob bridge and the assessment of several other bridges revealed the consequences and associated cost and emphasized the urgent need to improve the design rules for structures to avoid serviceability problems in the future. In response to these events, new research initiatives were undertaken in order to improve creep and shrinkage prediction models and to develop improved design guidelines and codes with respect to the time-dependent analysis of concrete structures. The prediction of time-related deformations in concrete is complex since it depends on many physical phenomena. The long-term behaviour of the structure shows large variations depending on the mix proportions, the type of cement, notional size, aggregates, local environment, the load history etc. Despite the large amount of research over the past decades, the underlying physical mechanisms of creep are however still not fully understood. A variety of prediction models for creep and shrinkage have been derived generally through statistical regression analysis of extensive experimental research test data. Guidelines for the prediction of creep and shrinkage behaviour of a plain concrete section are incorporated in codes and recommendations of international associations. Many models have been suggested to be used in structural calculations, such as: CEB-FIP Model Code 1990, fib Model Code 2010, EN1992-1-1:2005, ACI Committee 209, British Standard BS 8110, GL2000, AASHTO 2007, Model B3 and Model B4. One of the challenges is to model the influence of creep on the deflections accurately and efficiently. Concrete beams are subject to changes for a long period of time, during which creep and shrinkage of the concrete and relaxation of the prestressing steel develop. These effects cause additional deformations and redistributions of stresses. The local deformations within a cross-section can attain values several times larger than the initial elastic deformations and this can cause undesired serviceability problems and eventually damage in structural members over its lifetime. The prediction of time-dependent deformations is often complicated due to complex construction procedures characterized by numerous sequences of application of external actions and changes in the structure itself due to segmental or sequential construction techniques. In order to make accurate predictions of the deformations, it is important to take the time-dependent behaviour of the concrete element into account as accurately as possible. The design and analysis of concrete structures in Europe is performed using simplified calculation methods based on the Eurocodes. Advanced modelling techniques are becoming more accessible for the realistic evaluation of the delayed deformations of concrete and enable designers to more realistically analyse concrete structures using computer programs, accounting for the non-linear material behaviour and the time-dependent effects. During this PhD research, computational simulations were performed employing different concrete creep and shrinkage models to investigate the long-term deformations and stress distributions of reinforced and prestressed concrete beams. The practical applicability of several time-dependent structural analysis methods to model the creep behaviour of reinforced and prestressed concrete elements was investigated, i.e. employing simplified analytical expressions, a cross-sectional method and the direct stiffness method. The first chapter of the dissertation presents an overview of the time-dependent behaviour of concrete in general and an overview of the commonly used creep and shrinkage prediction models. Additionally, the common approaches to predict the time-dependent response of complex loading histories are explained, such as the use of rheological creep models and the use of the age-adjusted effective modulus method. In chapter II, an overview of historical datasets available in the Magnel-Vandepitte Laboratory archive is presented. The datasets relate to a unique and extensive Belgian research campaign with respect to the influence of creep and shrinkage on the long-term behaviour of reinforced, prestressed and partially prestressed concrete beams subjected to permanent loads during a period of 4.5 years. The dataset includes reinforced concrete beams and (partially) prestressed concrete beams tested in the period 1967-1987 and provides information regarding the concrete composition, creep and shrinkage behaviour, material properties and monitored strains and deflections. The third chapter focusses on several time-dependent structural analysis methods for concrete structures. The structural analysis problem regarding creep and shrinkage for the deflection verification of concrete structures can for example be solved by using analytical expressions, a cross-sectional approach or the direct stiffness method. Simplified analytical expressions were derived in this chapter for the prediction of deformations of reinforced and prestressed concrete elements. The chapter also presents a cross-sectional analysis method using the layered Euler-Bernoulli beam theory to account for non-linear material behaviour and non-linear creep strains, allowing more accurate predictions of the internal stress redistributions and the long-term deformations of structural members in case of concrete elements subjected to high levels of sustained loads. Additionally, an adaptation is made to the direct stiffness method in which the concrete creep behaviour is efficiently incorporated using a rate-type creep law described by Dirichlet series allowing fast predictions of the time-dependent behaviour of concrete elements. Chapter IV focusses on the application of the time-dependent structural analysis methods described in chapter III to the large-scale experimental programme available at the Magnel-Vandepitte Laboratory concerning the time-dependent behaviour of reinforced, prestressed and partially prestressed beams under different levels of loading, cross-sections, reinforcement ratios and degrees of prestressing. The measurement data of the tests regarding deflections and strains of the reinforced and prestressed beams are compared with the results of numerical analyses. In chapter V, the uncertainties on deflections and concrete stresses of a prestressed concrete beam were determined. The deflection of prestressed elements is the result of the application of external loads and the prestressing of the tendons, which are two opposing actions (with respect to deflections). The resulting total deflection of the concrete element is very sensitive to small changes to the input variables used for design. A design method with respect to these long-term deflections is proposed in which the deflection and stresses during the lifespan of the prestressed elements are limited by defining requirements for the prestressing arrangement taking the uncertainties of the input parameters into account. An example of a prestressed beam is given in which the deflection is verified over the beam’s lifetime using the proposed design method and an optimized design is proposed. Chapter V also describes a framework for the estimation of unknown input data using Markov-Chain Monte Carlo simulations. When one or more input-parameters of the prediction model such as loading history or environmental conditions are unavailable, an estimation of the probability distribution of these unknown parameters of the hierarchical numerical model can be obtained inversely on the basis of test measurements. The sixth chapter discusses a simplified model for drying shrinkage and the determination of shape correction factors. The drying shrinkage of ordinary concrete elements is predicted in engineering practice using a set of algebraic formulations proposed in international standards or guidelines. The use of these simple algebraic formulations is a reasonable compromise between simplicity and accuracy. For example, Eurocode 2, fib Model Code 2010, ACI, GL2000, Model B3 and Model B4 describe such models. However, these existing formulations in standards have a number of shortcomings as these empirical models inadequately account for the complex geometry of actual structures, exposure conditions, variability of envi