Three-dimensional finite element formulation for nonlinear dynamic analysis of seismic site and structure response

A three-dimensional finite element model for nonlinear dynamic analysis of seismic site and structure response is proposed and discussed. A series of numerical examples are presented which include modelling of a reinforced concrete frame with a portion of the ground consisting of various horizontal layers resting on rigid bedrock. The theoretical framework of the numerical analysis is based on continuum mechanics and irreversible thermodynamics. The spatial discretisation is performed by a combination of linear tetrahedral (ground) and hexahedral (structure) finite elements. The time integration is carried out by the leap-frog method. Total Lagrange formulation is adopted to account for large rotations and large displacements. To account for cracking and damage of the concrete, the frame structure is modelled by the microplane model. Damage and cracking phenomena are modelled within the concept of smeared cracks. Plasticity model is used for the modelling the reinforcement and the ground adopting the Von Mises and Drucker-Prager yield criteria, respectively. The influence of the ground layer configurations on the structure response is investigated and discussed. Comparative analysis shows the importance of the soil-structure interaction effects and material nonlinearity. Furthermore, with the implemented microplane model, which is aimed to be used for fracture and damage analysis of concrete, it is possible do assess the sustained structural damage.