In situ free-vibration tests on unrestrained and restrained rocking masonry walls

In the out-of-plane assessment of rocking walls, a relevant and yet uncertain aspect is the influence of energy dissipated during motion due to impacts and restraints, such as a floor or tie rods. Therefore, in situ rocking tests on unrestrained and restrained unreinforced masonry walls, made of composite (rubble + blockwork) masonry, were performed and analyzed. The restraint is given by steel springs of assigned stiffness, simulating a floor connected to full-scale (4×1×0.6 m3) specimens from a dismantling building. The specimens are displaced from a static equilibrium position and released, allowing to evaluate energy dissipation. The coefficient of restitution is estimated as the square root of consecutive peak velocities of the same sign, to take into account non-homogeneities in walls. For unrestrained walls, experimental coefficients of restitution vary between 81 and 88% of analytical ones, confirming the latter as conservative. For restrained configurations, experimental coefficients of restitution are between 74 and 83% of analytical values of unrestrained walls. Hence, an additional energy damping can be ascribed to the springs. Equivalent viscous damping ratios of a non-linear rocking system are calculated by considering a velocity logarithmic decrement, resulting between 6 and 8% (unrestrained condition) and between 8 and 10% (restrained condition). An analytical formula is proposed for estimating the coefficient of restitution for restrained walls if the dynamic properties of the unrestrained wall and the horizontal restraint are known. Finally, the relevance of a refined estimation of energy dissipation is discussed by means of numerical time history analyses.