Damage performance and failure analysis of reinforced concrete doubly curved shells under seismic excitations considering curvature and thickness variation

Most of the past investigations on the structural response of the doubly curved shell (DCS) roofs under seismic excitation were limited to linear dynamic analysis, whereas nonlinear dynamic analysis was rarely introduced, making it difficult to understand their dynamic behavior and draw general conclusions. Therefore, in the current study, linear dynamic analysis (LDA) and nonlinear dynamic analysis (NLDA) are conducted in tandem to fill the gap in the literature and give a complete perception of how these roofs respond to earthquakes. To this end, an innovative automatic finite element-based design algorithm is developed to obtain the steel reinforcement in preparation for the NLDA. Accordingly, the current study exploits the multi-layered shell element incorporated with the multi-axial concrete damage plasticity model (implemented via VUMAT subroutine) and the developed design algorithm (via Python script) to perform the NLDA and accurately capture the structural response and damage performance of these roofs. Unlike most common structures, the results demonstrated that DCS is highly affected by the vertical component of the earthquake rather than the horizontal component. The NLDA revealed that the shell exhibits severe damage and a high displacement response under strong seismic excitations, which could not be captured via the LDA. Additionally, the failure analysis is performed for the studied roof, considering the variation in shell curvature and thickness. This analysis shows a notable decrease in the demand-capacity ratio and steel rebar’s stress with increasing the shell curvature. Consequently, according to the proposed performance levels, the shell’s state changed from the initial failure to the elastic state. In contrast, slight changes in the overall behavior are observed due to the variation in the shell thickness. Finally, a new formula is proposed to predict the damage induced in the DCS under seismic excitations.