Implicit/explicit multi-time step co-computations for predicting reinforced concrete structure response under earthquake loading

Abstract

The paper explores the GC (Gravouil and Combescure) partitioning strategy recently adopted in real-time testing (RTDS) and pseudo-dynamic testing (PsD) with dynamic substructuring. The GC method is a multi-time step subdomain algorithm able to couple any time integration schemes from the Newmark family with the appropriate time step size dependent on the subdomain. The partitioning method is numerically tested by developing an external software able to couple finite element codes based on implicit and explicit time integration schemes. A complex Finite Element mesh partitioning, exhibiting a large number of interface points, has been considered for a full-size reinforced concrete frame structure subjected to an earthquake loading: the well-known SPEAR structure pseudo-dynamically tested at the ELSA laboratory, in Ispra, Italy. Implicit and explicit parts of the structure are modelled using multi-fibre beam elements whose cross-section is divided into steel and concrete fibres associated with cyclic and nonlinear behaviours. The accuracy of the results from the Explicit/Implicit multi-time step co-computation has been proved by comparing with the results from full explicit and full implicit computations. Despite the very large duration of the earthquake excitation and the number of interface nodes involved into the mesh partitioning, the Explicit/Implicit multi-time step co-computations provide very accurate global (displacements, forces at the base) and local (maximum strains in concrete) results while reducing by a factor 2 the computation times. Finally, it has been observed that the dissipated energy at the interface coming from the GC coupling algorithm remains very low at the end of the earthquake loading, less than 2% of the external energy, for time step ratios between the large and fine time steps ranging from 20 to 200.