Validation of the Discrete Element Method for the Limit Stability Analysis of Masonry Arches

This chapter revisits the limit equilibrium analysis of masonry arches when subjected to gravity and lateral loads. Firstly, the major contributions during the last three centuries either with geometric or energy formulations are discussed, and subsequently, the performance of the Distinct Element Method (DEM) is examined against rigorous solutions. Analytical solutions with the use of energy methods are presented for the assessment of the stability of masonry arches with circular or elliptical shapes under various load conditions, including gravity, lateral inertial loading or earth pressures. The DEM is implemented in all loading cases and reproduces the analytical results with remarkable accuracy. The DEM is used either for a direct correlation with the classic limit analysis that assumes that the joints of the masonry blocks do not transmit tension, masonry blocks are rigid and incompressible and do not slide at the joints, or by permitting sliding with the adoption of Coulomb sliding failure between the joints.