The relevance of energy damping in unreinforced masonry rocking mechanisms. Experimental and analytic investigations

Abstract

Existing unreinforced masonry buildings frequently suffer out-of-plane local collapse mechanisms when undergoing earthquake ground motion. The energy damping that occurs during the motion, due to impacts of a wall against the foundation or against other walls, is a relevant parameter on the response. An experimental investigation has been carried out to estimate the dissipation of kinetic energy that takes place during free oscillations. Restraint conditions allow for two-sided rocking (wall resting on a foundation) and one-sided rocking (wall resting on a foundation adjacent to transverse walls). Five specimens have been tested, modelling walls acted out-of-plane (fa double dagger ades). When one-sided rocking is under consideration, different depths of the contact surface between fa double dagger ade and transverse walls are considered. In the case of two-sided rocking, the experimental coefficient of restitution is slightly lower than the analytic coefficient. In the case of one-sided rocking, an analytic formulation is proposed and this is compared against experimental data. Although the coefficient of restitution of one-sided rocking is less than half that of two-sided rocking, it is not equal to zero. Thus, it cannot induce a sudden stop of the motion. Hence, nonlinear time history analyses performed under this assumption may prove unsafe. Moreover, a comparison has been carried out between overturning maps, induced by twenty natural accelerograms, computed for the analytic coefficient of restitution and those computed for the experimental coefficient of restitution. The increased energy dissipation reduces the frequency of overturning and causes a more regular behaviour

Energy Dissipation Involved in the Out-of-Plane Response of Unreinforced Masonry Walls

“…A common approach, relying on the classical hypothesis of the impulse dynamics, is simulating the energy dissipation involved in such mechanisms through a coefficient of restitution [4][5]20]. Another option is adopting an equivalent viscous damping approach defining a velocity dependent damping force through a constant, variable (with cycleto-cycle iterations) and stiffness proportional damping ratio.…”

Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments

“…Indeed, the body not being fully rigid, the moment of momentum was not conserved. In this line, also Sorrentino et al [22] carried out an experimental campaign on URM solid clay brick or tuff specimens for two-sided and one-sided motion, with height to thickness ratios varying between 6.5 and 14.6. The authors found values of the restitution coefficient equal to 95% of the theoretical value.…”

“…In [20], a probabilistic approach was suggested to solve this issue. As concerns sliding, the absence of it is acceptable when the static coefficient of friction is larger than the ratio b/h [22,28]. Generally, masonry walls have this ratio much lower than the static friction coefficient, usually equal to 0.6-0.7 [28].…”

Shaking Table Tests on Unreinforced Load-Bearing Masonry Walls – Comparison With Simple Rocking Models.

“…This impact obviously dissipates energy. The approach proposed by Housner to account for the dissipation is to consider the conservation of angular momentum with various assumptions (see [7]). According to this, a reduction factor e is defined and has to be applied to the velocity of the wall before the impact to obtain the velocity right after this impact.…”

“…The formulation of the restitution coefficient used in the basic reference model is the one proposed by [7] deduced from the theory developed by Housner. An alternative formulation is however proposed by [8], also on the base of the Housner theory, that can in the present case be further simplified according to the specific expression of I O :…”