Quantifiable feasibility check of masonry assemblages composed of interlocking blocks

This paper introduces a digital tool to quantify the structural feasibility of single layer assemblages of interlocking blocks. These have corrugated faces to keep the blocks together and prevent them from sliding through the frictional and shear resistances of the locks in two orthogonal directions. Calling the sliding constraint violation of an equilibrated model "sliding infeasibility", it is measured as a numerical value, named sliding infeasibility measure (SIM). The designer, instead of removing the infeasibility by trial and error, can adjust the assemblage geometric parameters to minimise the SIM. To this aim, first the structural soundness of an assemblage is investigated through the equilibrium analysis accounting for two sliding behaviours. This method is validated by comparing some thinnest feasible models with conventional blocks existing in the literature and the same models with interlocking blocks. Then, as the core of this paper, the equilibrium analysis is reformulated to develop an optimization problem aimed at quantifying and minimising the SIM. Rearranging the sliding constraints, the tool measures the tangential internal forces violating the sliding valid range as the SIM. Since more than one solution can exist for an equilibrated tensionless model with sliding infeasibility, this problem finds the solution for which the tangential forces are the closest to the valid sliding ranges. The method is validated by comparing the SIM to the structural soundness of assemblages with different interface geometric properties. Finally, the tool performance to design shells with arbitrary shapes is demonstrated through several examples.