The main purpose of this work is to understand the structural characterization of reinforced concrete slabs under near-field and contact explosions using the developed rate-sensitive damage model. The model is developed based on the experimental observation to include the effects of strain rate and damage rate. It is observed that with increasing strain rates there is a decrease in damage evolution due to artificial stiffening effects and the final level of damage is higher. This is achieved by using a power law model to relate the rate of damage to the equivalent plastic strain rate. The concrete undergoes pulverized damage because of the loss in cohesive strength at higher hydrostatic stress. Thus, the hydrostatic damage has to be considered along with tension and compression damage parameter. Strong volumetric deformation of the material that includes the hydrostatic and compaction damage is also accounted for in the model. The size of the yield surface increases with strain rate and is capped with an upper limiting value. The incremental effective stress–strain relationships are defined in terms of rate of damage, accumulated damage and viscosity parameters reflecting the inherent physical inertial, thermal and viscous mechanisms respectively. The results from the numerical analysis are found to match well with experimentally observed results. © 2023, The Author(s), under exclusive licence to Springer Nature B.V.