Analytical Models for the Rocking Response of Stacked, Keyed Graphite Blocks in the Core of a High-Temperature Gas Reactor

The core of the Boston Atomics-designed horizontal compact high-temperature gas reactor (HC-HTGR) is composed of columns of stacked, keyed graphite blocks. The dynamic response of these columns is predominantly governed by rocking, which has been investigated through shake-table experiments at the University at Buffalo. Building on insights gained from the experiments, this paper develops theory for the dynamic analysis of stacked, keyed graphite blocks under horizontal earthquake shaking. The analytical model is formulated as a state-space system, offering first-principles predictions of system-level responses, including lateral displacement and rotations of stacked column of blocks. Controlled conditions are implemented to enable transitions between different state-space equations based on the active rocking interfaces, the number of blocks rocking together, and the column geometry, thereby facilitating the consideration of relative rotations occurring at multiple block interfaces as the column displaces laterally. Energy dissipation is modeled using a velocity reduction coefficient, a parameter serving as a proxy for all energy loss mechanisms in the system, including frictional contact, vertical impacts during rocking, and material damping. The optimal values for this coefficient are calibrated using test data of various column configurations, representative of those in the core of the HC-HTGR. The accuracy of the models is evaluated for more than 100 cases, covering columns of varying heights and shaking directions and a range of harmonic and seismic inputs. A subset of the results is presented in this paper. Predictions of peak column displacements and block rotations are within 15% of the experimental measurements, with closely agreeing transient response histories. These analytical models provide useful first-principles predictions to verify numerical models of columns of keyed blocks, which are to be used for analysis of complex core geometries, and considering three-component earthquake shaking, for which developing analytical models is highly complex and often impractical.