Enhanced Prediction of Rocking and Sliding of Rigid Blocks Using a Modified Semi-Analytical Approach and Optimized Finite Element Modeling

Accurate prediction of the rocking and sliding response of free-standing rigid blocks under seismic excitation remains challenging, particularly in regimes where rocking and sliding are strongly coupled and motion mode transitions occur. This study presents a modified semi-analytical framework and an optimized Finite Element Method (FEM) approach to investigate the nonlinear dynamics of rigid rectangular blocks subjected to initial angular displacements, assuming Coulomb friction and near-inelastic impacts. The proposed semi-analytical formulation explicitly captures the coupling between rocking and sliding motions, enabling systematic identification of rest, rocking, sliding, rocking–sliding, and free-flight response modes. Benchmark comparisons with Veeraraghavan’s classical model show overall agreement in limiting cases but reveal notable differences in intermediate regimes, where motion mode transitions are highly sensitive to friction coefficient and slenderness ratio. These discrepancies arise from the ability of the present formulation to resolve transitional rocking–sliding behavior that is not fully represented in uncoupled or limiting-case assumptions. Complementary FEM simulations employing both rigid and deformable body representations further elucidate the role of contact modeling and energy dissipation. While rigid-body FEM models offer computational efficiency, they exhibit localized penetration and residual bouncing due to contact enforcement limitations. In contrast, deformable FEM models more closely approximate near-inelastic collision behavior and dissipate impact energy more effectively, albeit at higher computational cost. The combined semi-analytical and FEM results provide a robust framework for interpreting motion mode transitions, quantifying contact and penetration effects, and defining the applicability limits of simplified rigid-body models. These findings offer practical guidance for selecting appropriate modeling strategies for seismic response assessment of free-standing rigid blocks.