Irrecoverable Collapse Time for a Fixed-Hinge Dry-Stack Arch Under Constant Horizontal Acceleration

The collapse of dry-stack masonry arches results from the transformation of a static system to a mechanical state through the development of mechanical joints. The traditional failure condition is this mechanization through the formation of four-hinges in a kinematically admissible configuration. The first-order analysis of an arche’s seismic capacity is obtained through limit analysis (LA) approaches. One approach is the equilibrium assessment of the kinematic theorem through the use of a kinematic collapse load calculator (KCLC). Utilizing a custom KCLC developed and validated from an experimental arch, with the added control of the single degree-of-freedom rotations, an analytic solution is developed between the applied acceleration and the minimum time duration required for collapse. The collapse multiplier and arch centroid data is recorded for all the admissible conditions that exist in the spatial deformation propagation. From this information, the work required to collapse the arch under kinematic equilibrium is established and utilized to decompose the static and kinematic energy contributions. The time-displacement domain is then defined from the resulting kinematic energy of the overloaded arch and used to evaluate the time where the kinematic energy exceeds the remaining work required for the loss of the kinematically admissible condition. This results in a simple analytical function linking excess static acceleration with a time limit of recovery.