Pieterjan Criel

Modelling of Long-Term Loading Tests on Reinforced Concrete Beams

During the period 1967-1985 the Magnel Laboratory for Concrete Research participated in an extensive Belgian research campaign with respect to the influence of creep and shrinkage on the long-term behaviour of reinforced and prestressed concrete beams. This research campaign, jointly conducted at several Belgian research institutes, comprised the investigation of concrete and reinforced concrete beams (phase 1), prestressed concrete beams (phase 2) and partially prestressed concrete beams (phase 3). The main aim of the research campaign was the determination of the long-term behaviour subjected to permanent loads, considering the influence of the magnitude of the loads, different reinforcement ratios and/or prestressing degrees and/or different cross-sectional shapes. These results were obtained by a joint collaboration of 4 Belgian research institutes, each focussing on a different reinforcement ratio and reinforcement arrangement. With respect to the reinforced concrete beams (phase 1), at each institute 12 beams were tested in a 4point bending configuration, namely 2 static tests at 28 days and 10 long-term tests with a duration of 2 to 4 years, considering different loading levels. In this contribution some results of the reinforced concrete beams (phase 1) will be documented and analysed, comprising the results obtained on 48 reinforced beam specimens with a length of 3.4 m (span of 2.8 m) and cross-section of 0.28 m x 0.15 m. A cross-sectional calculation tool developed at our department – incorporating the current creep and shrinkage models in standards and guidelines – will be employed in order to investigate the accuracy of the available models with respect to their ability to predict the structural behaviour of the documented reinforced concrete beams.

Contemporary Analysis and Numerical Simulation of Revisited Long-Term Creep Tests on Reinforced Concrete Beams from the Sixties

The stresses and deformations in concrete change over time as a result of the creep- and shrinkage deformations of concrete. Different material models are available in literature in order to predict this time-dependent behaviour. These material models mostly have been calibrated on large datasets of creep specimens. In order to verify the accuracy of the contemporary material models with respect to the prediction of the creep behaviour of reinforced concrete beams, a cross-sectional calculation tool which employs the age-adjusted effective modulus has been developed and used to analyse an original set of 4 year-long creep data on reinforced beams from the 1960’s. Six commonly used material models for the prediction of creep and shrinkage are considered in the current investigation: CEB-FIP Model Code 1990–1999, fib Model Code 2010, the model of EN1992-1-1, model B3, the Gardner Lockmann 2000 model, and ACI 209. The data on reinforced beams relates to an experimental investigation in collaboration with six major research institutes in Belgium. From 1967 until 1972 thirty-two reinforced beams with different reinforcement ratios were subjected, up until 4.5 years, to different stress levels in a four point bending configuration with a span of 2.8 m. In this paper a comparison between the measurements and the calculated deflections and strains is reported. Further, the deflections were also predicted using the contemporary creep models in combination with the nonlinear creep correction factor provided in EN1992-1-1, since the maximum concrete stresses in the beams were outside the service stress range of each of the models. Correcting for the nonlinearity of the creep coefficient significantly improves the calculated deflections. The most accurate predictions of the deflections at early age were obtained by the model of fib Model Code 2010. The Gardner Lockmann 2000 model exhibits the highest accuracy with respect to deflections at the end of loading and with respect to the creep rate.

Shape Correction Factor for Drying Shrinkage in a Concrete Cross-Section

A concrete member is subjected to loads for a long period of time, during which creep and shrinkage of concrete develop gradually. The prediction of this time-dependent behaviour is important as it may cause serious serviceability problems in concrete structures. A time-dependent analysis is commonly based on empirical equations according to design codes where the function describing the time dependent increment of shrinkage and creep is commonly, among others, defined based on the notional size of the element. In case of imbedded steel or insulated boundaries the moisture transport can be partially affected or prevented. Also, the geometry and size of the cross-section have an important effect on the shrinkage behaviour of a concrete member. Hence, the performance of commonly used empirical formulas may be improved by applying a correction factor on the notional size. In order to investigate the impact of these various factors on the net macroscopic shrinkage used in analysis and design, a discretized 2D physical model was developed. The model was used to simulate drying of a concrete cross-section by determining the moisture distribution in the cross-section as function of time.

Uncertainty quantification of creep in concrete by Taylor expansion

Abstract If deterministic creep prediction models are compared with actual measurement data, often significant differences can be observed. These inconsistencies are associated with different causes, i.e. model uncertainty, uncertain input parameters, measurement errors and wrongfully applying creep prediction models outside their limitations. First, the physical mechanism causing creep of concrete is not yet fully understood. Therefore, it is very likely that certain influences on creep of concrete are not considered in these prediction models, resulting in systematic model errors. The model errors can be quantified by comparing prediction results with experimental data. Secondly, the stochastic character of the input parameters form an additional source of uncertainty which can be quantified by the variance of the model response. The coefficient of variation in function of time-duration, i.e. the time since the application of the load, is a useful measure to quantify the level of uncertainty. In the literature, statistical analysis by means of numerical simulations are often used for this matter. However, even for specialized sampling techniques, a large amount of samples is necessary to cover the relevant ranges of various input parameters. The aim of the present study is to provide an approximate uncertainty quantification of the creep prediction models given uncertain input parameters. This approximation is based on a Taylor series approach. This approach has the advantage that is does not require numerical simulations nor does it require the knowledge of the probability density function of the input parameters. This method is evaluated and compared with the statistical analysis for several creep prediction models available in literature and design codes.

Computationally efficient estimation of the probability density function for the load bearing capacity of concrete columns exposed to fire

Concrete columns are critical for the stability of structures in case of fire. In order to allow for a true Performance Based Design, the design should be based on considerations of risk and reliability. Consequently, the probability density function (PDF) which describes the load-bearing capacity of concrete columns during fire exposure has to be assessed. As second order effects can be very significant for columns, traditional probabilistic methods to determine the PDF become very computationally expensive. More precisely, for most current numerical calculation tools (e.g. Finite Element), the computational requirements are so high that traditional Monte Carlo simulations become infeasible for any practical application. In order to tackle this, a computationally very efficient method is presented and applied in this paper. The method combines the Maximum Entropy Principle together with the Multiplicative Dimensional Reduction Method, and Gaussian Interpolation, resulting in an estimation of the full PDF requiring only a very limited number of numerical calculations. Although the result is necessarily an approximation, it gives very good assessment of the PDF and it is a significant step forward towards true risk- and reliability-based structural fire safety.

Stress redistribution of concrete prisms due to creep and shrinkage: long-term observations and analysis

In 1979, 16 concrete prisms with dimensions 140x150x4000 mm were casted in the Magnel Laboratory for Concrete Research. These prisms differ by the amount of passive reinforcement and by the applied loading level. Four reinforcement ratios were considered, i.e. 0%, 1.5%, 3% and 6%. For each reinforcement ratio a prism was subjected to an axial load corresponding to a concrete stress of 0, 5, 10 or 15 MPa. The combination of both parameters results in a total of 16 specimens. The compressive stress was applied to the prisms by means of post-tensioned unbonded strands at an age of 28 days. The stress level was kept constant during the first 12 years of the experiment by re-adjusting the force in the strands when the deviation exceeded 2% of the initial value. Afterwards, no re-adjusting of the strands took place. Significant redistribution of the stresses between the concrete and the steel can be expected due to the creep and shrinkage of concrete. This redistribution is larger for the prisms with a higher reinforcement ratio, resulting in lower creep and shrinkage strains. The time-dependent response of these prisms was modelled taking into account the prestress losses and stress redistribution between the concrete and the steel. For reasons of numerical efficiency, the compliance function was approximated by a Dirichtlet series using continuous retardation spectra. A comparison between the predicted results and the measurements is given for two prisms.