A number of artificially generated earthquake time-histories (AGETH) fitting to a Eurocode 8 (EC8) response spectrum are randomly generated using SIMQKE software and the average generated spectrum compares well with the EC8 one. Two Finite element (FE) smeared crack models, named Multi-crack and Craft, are well validated against experimental data of concrete and Reinforced concrete (RC) structures under monotonic and cyclic loadings. They are then used in the analysis of RC bridge piers under the AGETH. Several techniques including Fourier analysis, normalised cumulative spectrum, energy dissipation, damage index as well as probability applications are applied to quantify the structural response and damage. Based on the convergence of the representative responses under different numbers of AGETH, a minimum representative number of AGETH from 6 to 11 may be sufficient depending on the confidence band width from the mean of all damage responses. Effects of several parameters of the earthquake and structure to the dynamic response and damage of the bridge pier are investigated. Throughout these parametric studies, several of the common circumstances that structural engineers face are addressed and the proposed number of artificial earthquake time-histories required for non-linear dynamic analysis is thereby validated.