A 2016 project utilized a variety of Structural Integrity competencies to analyze a beyond design basis threat at an overseas nuclear power plant. The client was assessing a plant design and approached Structural Integrity to investigate local perforation and scabbing of a reinforced concrete wall due to hard missile impact. Perforation occurs when a missile fully penetrates and passes through a target while scabbing occurs when material is ejected from the back face of a target, potentially striking personnel and equipment inside the facility.
The client also sought to reduce the volume of wall reinforcement, a potentially large cost savings, while still meeting the facility’s strict design criteria. The project is best described in four stages and took advantage of our AIA experience, finite element (FE) modeling expertise, and proprietary concrete constitutive model ANACAP.
The impacting missile was an airplane engine traveling at high velocity. A quarter-model of the engine (Figure 1) was developed through a three-step benchmarking process. First, the model’s inner core was developed through an iterative process by benchmarking the core’s post-impact residual velocity to Nuclear Energy Institute (NEI) available estimates. The inner core model was “launched” at concrete walls with various thicknesses, concrete strengths, and with various initial velocities to ensure that the inner cores’ behavior matched predicted estimates within empirically tested limits (Figure 2). Models of the nacelle assembly and turbofan were developed in the second step using a similar benchmarking process. Finally, the Riera methodology  was used to compare the FE model’s behavior to analytical estimates (Figure 3).
A metric was needed to determine if concrete scabbing would occur during impact and, if so, its extent. NEI equations were used to determine at what velocity scabbing is expected to occur when a cylindrical missile (such as the inner core) is “launched” at various concrete walls. These velocities were used as inputs in FE models of the inner core to develop a metric that predicts when concrete scabbing is expected to occur.
This metric was verified by developing an FE model, which recreated a 1989 experiment performed as part of AIA qualification by the Central Research Institute of Electric Power Industry . The experiment utilized scaled tests of hard missiles impacting reinforced concrete slabs and produced data relating to the slabs’ structural resistance to missile perforation. The experiment also documented the extent of scabbing on the walls’ non-impacted face. Structural Integrity’s scabbing metric accurately predicted the extent of scabbing seen in the experimental results.
Having developed a FE representation of the impacting engine and a metric to determine the extent of concrete scabbing, the benchmarked engine was “launched” at the design wall. The cover concrete on the non-impacted face was monitored for scabbing. Plastic strains in the embedded reinforcement were also monitored (Figure 4). The analysis showed that the scabbing metric was not exceeded under the design conditions, and as such, there was good confidence that scabbing was not expected to occur.
Since scabbing was not expected to occur in the design wall, an optimization study was performed to determine if alternative cost-saving configurations would also satisfy the design criteria. Three cost-saving configurations were investigated:
(a) a reduction in main/longitudinal reinforcement, (b) a reduction in shear/transverse reinforcement, and (c) a reduction in concrete design strength. A parametric study was undertaken to determine how the three configurations would respond to the engine impact under slightly perturbed design inputs. The study indicated that a reduction in the walls’ reinforcement or concrete strength would provide satisfactory behavior under best estimate (i.e., mean) conditions. An assessment utilizing higher confidence bands, typical of design basis assessments, showed that reducing the wall reinforcement may result in scabbing (Figure 5).
Structural Integrity utilized its AIA experience, finite element (FE) modeling expertise, and ANACAP concrete constitutive model to perform an optimization study that revealed that its client could meet nuclear facilities strict design criteria while reducing construction costs.