Seismic vulnerability prediction of masonry aggregates: Iterative Finite element Upper Bound limit analysis approximating no tensile resistance

A novel 3D Finite Element Upper Bound limit analysis approach for the evaluation of the seismic vulnerability of masonry aggregates when the collapse may occur both locally and globally is presented. The model relies on a 3D discretization of the aggregate by means of infinitely resistant hexahedron elements and rigid plastic quadrilateral interfaces, where all plastic dissipation occurs. The interface behavior is assumed isotropic, with friction, cohesion, and tension cutoff. The collapse horizontal acceleration is obtained in the discretized model solving large-scale linear programming problems with standard numerical routines. According to a consolidated literature, the vulnerability prediction should be done with preassigned failure mechanisms formed by large macro-blocks mutually roto-translating, and assuming a material unable to withstand tensile stresses without mutual sliding between macro-blocks. However, such assumptions may be responsible for an overestimation of the load-carrying capacity and the determination of a realistic mechanism is neither obvious nor possible in any case. Discretizing the aggregate into 3D elements and interfaces, the failure mechanism is automatically found in the solution of the limit analysis problem, but enforcing the no-tension material hypothesis may be responsible for the activation of parasite sliding between contiguous elements or stalling issues of the numerical algorithm. In the first case, the failure mechanism changes considerably and the computational evaluation of the horizontal acceleration at collapse can be affected by unsafe inaccuracy. The present approach iteratively approximates the no-tension material model at low computational cost, progressively shrinking the failure surface and evaluating (i) collapse accelerations, (ii) failure mechanisms active, (iii) power dissipated on interfaces and (iv) power expended by loads not dependent on the collapse multiplier. By analyzing the failure mechanisms obtained, it is possible to select where spurious sliding is not dominant. Enforcing to zero the power dissipated on interfaces it is possible to estimate the collapse multiplier corresponding to the twofold assumption that (i) parasite sliding is negligible and (ii) the material approximates in a technically acceptable way the no-tension one. The model is first benchmarked on a masonry portal, where a reference solution is available, and then applied to two historical aggregates located in Italy.