Advanced energy-based and two-degree-of-freedom analytical modeling of reinforced concrete slabs subjected to...

When reinforced concrete (RC) slabs are subject to low velocity impacts (LVI), they will experience highly non-linear behaviors based upon the combined effects of flexural deformations; tensile membrane actions; punching shears; and local crushing as well as the evolving nature of damage in these structures. Most analytical models have been developed under restrictive simplifications; lack complete partitioning of energies; and depend heavily upon computationally intensive finite element simulations. An analytical-energy-based approach is presented to predict the non-linear dynamic behavior of RC slabs subjected to both LVIs and equivalent blast loads. The proposed model integrates an improved two degree-of-freedom (2-DoF) dynamic interaction system with an explicit multi-mechanism energy partitioning procedure which can be used to quantify all of the major forms of energy consumption including flexural; membrane; shear; crushing; damping and damage. The analytical framework has incorporated strain rate enhancement through use of dynamic increase factors (DIFs); punching shear capacity through application of the critical shear crack theory (CSCT); and geometrically non-linear membrane behavior via Xie's formulation for large deflection membrane behavior. A wide-ranging parametric analysis was performed to examine the effect of impact energy; slab thickness; reinforcement ratio; boundary conditions and advanced materials systems such as normal strength concrete (NSC); ultra high-performance concrete (UHPC); and ultra high-performance fibre reinforced concrete (UHPFRC). Results indicated that an increase in the magnitude of impact energy from 1 to 6 kJ resulted in an approximate 301% increase in slab displacement. Furthermore, an increase in the slab thickness from 60 to 125 mm resulted in a reduction of approximately 68% in slab displacement. It was also found that when compared with RC slabs made with NSC, those made with UHPFRC had displacements decreased by approximately 61% and reduced damage dissipation energy by approximately 69% due to higher levels of crack bridging and membrane resistance. Lastly, it was determined that twisted and hooked end fibres had the greatest energy absorbing capability and provided the longest delay to punching shear failure. Validation studies were conducted against existing experimental data and comparative non-linear ABAQUS CDP simulations indicating prediction error margins generally less than ± 5-10% and good correlation in terms of slab displacement response; crack development; and failure progression. The validation studies also showed that the method could be easily adapted for equivalent blast load analyses using impulse equivalency principles thus enabling a rapid predictive tool for designing RC slab systems resistant to either low velocity impact or blast loads.