Applicability of Sub-Modelling Technique for Dynamic Analysis of Concrete Structures With Attached Equipment Under Missile Impact

Abstract This paper describes the work conducted by the Canadian Nuclear Safety Commission (CNSC) related to the numerical simulations of reinforced concrete (RC) structures under deformable missile impact. The current paper is a continuation of the work conducted in the frame of the OECD/NEA* IRIS (Improving Robustness Assessment Methodologies for Structures Impacted by Missiles) Phase 3 benchmark project. The concrete mock-up with two simple structures attached, one welded and another bolted, was built and tested at the VTT Technical Research Centre in Espoo, Finland. This mock-up was impacted by three subsequent missiles with varying velocities in order to obtain the damage accumulation. To examine vibration transmission through the mock-up, the simple structures modelling equipment were attached to the rear wall of the structure, while the missile impact was at the centre of the front wall. The parameters of the missiles and the RC structure were selected to ensure a flexible behaviour of the RC target in the impact area with only moderate damages, specifically cracking and permanent deformation without perforation. The non-linear dynamic behaviour of the reinforced concrete slabs under missile impact was analyzed using the commercial FE code LS-DYNA. A hybrid FE model using both 3-D solid and 2-D shell FE models was developed for the target discretization. Since the ultimate objective of this work is to model the entire structure over long time periods, a simplified combined shell-solid model with distributed (smeared) reinforcement was selected and validated. This model employs solid FE around an impact area and shell FE for the rest of the mock-up. Detailed modelling of a large RC structure with all equipment attached leads to a very large finite element (FE) model. Therefore, two-level FE modelling using sub-modelling approach was employed: first, analyze the vibrations of a reinforced concrete structure with simplified equipment modelling, and second, analyze in detail the equipment connected to it. This approach assumes uncoupled dynamic behaviour of the structure and the equipment. While the sub-modelling technique is commonly used in static analysis, a special sensitivity analysis was conducted to prove the applicability of sub-modelling for impact analysis. Finally, the effect of structural damping was examined and the best possible damping was selected. The selected damping values and sub-models resulted in relatively good agreement with the test results for both global (RC mock-up) and local (equipment) behaviour.