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Sustainability means meeting the needs of today without compromising the needs of the next generations. How can we meet the needs of the next generations, if we do not even know what these needs are? If we do not listen to the next generation and learn from them? Do we even meet the needs of today for everyone on earth?
This paper presents a probabilistic methodology based on the thermo-mechanical finite elements analysis to investigate the impact of the variability of the thermal properties of the concrete in the fire safety of structures. This is meant to evaluate if characteristic values or safety factors for the conductivity and specific heat are required during the semi-probabilistic structural fire safety assessment. To illustrate the use of the proposed methodology, this work includes a case-study with a tunnel lining which considers the uncertainties related to the thermal and mechanical properties of the concrete, the soil load, and the temperatures described by the standard temperature-time curve. Two failure criteria are considered: one was the maximum temperature of 300 °C at the reinforcement and the other based on the temperature-dependent strength as provided in the Eurocode EN 1992-1-2. Several finite element analyses are performed. The design of experiments is executed by a Correlation Latin Hypercube Sampling. The calculated probability of failure has different values depending on the adopted failure criteria. A sensitivity analysis using the Spearman's rank correlation coefficient was carried out and demonstrates that the uncertainty related to the specific heat has the greatest impact on the results.
The durability of concrete structures and its performance over the lifetime is strongly influenced by many interacting phenomena such as e.g. mechanical degradation due to fatigue loading, loss of prestress, degradation due to chemical reactions or creep and shrinkage. Failure due to cyclic loading is generally not instantaneous, but characterized by a steady damage accumulation.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. A key limitation is that the models often do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles.
The objective of this paper is the presentation of numerical methods for the simulation of concrete under fatigue loading using a temporal multiscale method.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different time integration schemes.
Modeling the interactions of creep, shrinkage and damage in a multiphysics simulation of concrete
(2018)
The time dependent, mechanical behavior of concrete is affected by multiple phenomena like creep, shrinkage and damage propagation. The interactions of these processes are supposed to have significant influence on the materials response to external loading. For example it can be observed that the compressive strength of concrete rises with lowering the moisture content [Dahms, 1968].
Most of the constitutive models for finite element methods are designed with just a single phenomena in mind. In multiphysics simulations it is quiet common to use a linear superposition, i.e. additive decomposition of the total strain into elastic shrinkage, creep or thermal strains.
In this paper, the interactions of creep, shrinkage and damage models are investigated, in particular for cases where the assumption of linear superposition is questionable. A gradient enhanced damage model proposed by [Peerlings et al., 1996] is employed. Creep is modeled as a Kelvin chain as described in [Jirásek and Bažant, 2001]. Shrinkage is simulated by using two different approaches. The first model simulates shrinkage as an additional moisture dependent strain component. In the second model, shrinkage is simulated as a moisture dependent pore pressure applied to the solid bulk.
The impact of model interactions will be discussed with a focus on simulating the influence of the moisture content on the macroscopic strength. The model is validated by comparison to experimental data.