Prediction of the nonlinear dynamic behaviour of a concrete slab subjected to blast load

Abstract

With the rise of hydrogen as a green alternative for fossil fuels, the demand for storage capacity of hydrogen increases significantly. Due to the high risk of explosions in urban environments it brings along, the blast analysis of buildings within in range of the explosions becomes more relevant.

The goal of this research is to develop a quick method to analyse the roof of a building subjected to blast load. This is done by first clarifying the blast load definition on a reinforced concrete (RC) structural element through existing design standards and literature. Next, the material behaviour of the concrete and the reinforcement steel is scrutinised by an extensive literature study. Materials behave differently under dynamic loads. The dynamic material properties are increased by the strength increase factor (SIF) and the dynamic increase factor (DIF).

In blast analysis, most energy is dissipated though plastic deformation. Therefore, it is of great importance to accurately describe the nonlinear behaviour of RC elements. The nonlinear behaviour of RC elements is translated in the moment-curvature relationship. This relationship is calculated on cross-sectional level and serves as input for the global beam or slab model. The global structural behaviour of the beam or the slab is calculated using the finite difference method (FDM). The FDM model generates a force-deflection (F-u) relationship which can be used in the single degree of freedom (SDOF) mass-spring system. The SDOF mass-spring system is used in this research to predict the dynamic behaviour of RC elements.

The research method is validated by published experiments and finite element analysis. Three experiments are reported, where the following results are obtained:
• Flexural stiffness may be assumed when the scaled distance is above 1.2 m/kg1/3. This is labelled as the ‘far field design range’.
• When choosing the DIFs carefully, the dynamic behaviour of RC elements can be predicted well.
• The FDM model can provide a good estimation of the nonlinear F-u relationship. The method of incorporating cracks in the FDM model is not previously presented in published literature.
• The unloading stiffness requires additional care. This research briefly covers the unloading stiffness.
• According to the UFC 3-340-02 (Department of Defence, US, 2008), RC elements without shear reinforcement and without the possibility of membrane action, fail at a support rotation of 2 degrees. This is where crushing is supposed to happen. This research shows that this is rather conservative and that the support rotation can go up to 6 degrees before failure.

Finally, the validated research method is applied on a case study. The case study contains a slab supported on two stiff beams on opposing sides. This results in a main span (weak direction) and a secondary span (stiff direction) due to the flexural stiffness of the supporting beams. In most cases, the slab supported by beams can be approached as a SDOF mass-spring system. After occurrence of cracks, the slab reinforcement in the main span direction will absorb most of the energy and is therefore the dominating member in the two degrees of freedom (2DOF) mass-spring system.