Vulnerability of Pointed Masonry Barrel Vaults Subjected to Differential Settlement Simulated with a GPGPU-Parallelized FDEM

Abstract

Pointed masonry barrel vaults are widely used in classical historic structures, such as cathedrals and aqueducts, and they are very sensitive to differential settlement. These vaults are assemblages of masonry units and mortar. Since the bonding strength of mortar degrades over ages, dry-joint assumption is widely accepted. Failure behavior of dry-joint pointed masonry barrel vaults subjected to differential settlement is highly complex, discontinuous, and nonlinear. In this study, a 3D GPGPU-parallelized hybrid finite-discrete element method (FDEM), which is an advanced extension of finite element method (FEM) and discrete element method (DEM), is employed to investigate the capacity of pointed masonry barrel vaults subjected to differential settlement. When modeling barrel vaults with 3D FDEM, each masonry unit is discretized into a couple of four-node tetrahedral elements whose deformability is characterized by standard finite element formulation. Thus, structural deformation and interaction forces can be obtained in an accurate manner. Numerical examples are presented and validated with results from literatures. A base case is selected, and the influence of embrace angle ([Formula: see text], sharpness (Sh), stockiness (St), and out-of-plane length ([Formula: see text] on the failure behavior is parametrically investigated. The larger the [Formula: see text] or Sh, the smaller the ultimate settlement. The same applies to St in general, while an excessively large St results in small ultimate settlement due to sliding. The influence of [Formula: see text] can be mitigated should it is large enough compared with the span. It is demonstrated that the 3D GPGPU-parallelized FDEM is a robust tool for analyzing the vulnerability of pointed masonry barrel vaults subjected to differential settlement.