A combined experimental and numerical study: Linking vibration response to load carrying capacity of a masonry dome

In this manuscript, the authors present a combined experimental and numerical study that empirically links measured vibration response characteristics to the remaining load carrying capacity of a masonry dome as the structure is gradually damaged with discrete and distributed cracks. First, the three-dimensional, nonlinear finite element model of the dome is calibrated using both nondestructive vibration response measurements and destructive load displacement tests. The gradual development of major, discrete cracks is simulated by introducing a mesh discontinuity, while the development of minor, distributed cracks is incorporated by the inherent smeared cracking capability of the finite elements. The calibrated numerical model is used to estimate degradation in both the strength and stiffness of the dome, indicated by a reduction of the load carrying capacity, and by the reduction in natural frequencies, respectively. An empirical function is trained to link the reduction in natural frequencies (a quantity related to stiffness that is feasibly measurable), and the remaining load carrying capacity (a quantity related to strength that is not feasibly measurable) for spherical domes. This empirical relationship is generalized for spherical domes with different span-to-height ratios.