This paper aims to quantify the cumulative damage of unreinforced masonry (URM) subjected to induced seismicity. A numerical model based on discrete element method (DEM) has been develop and was able to represented masonry wall panels with and without openings; which are common typologies of domestic houses in the Groningen gas field in the Netherlands. Within DEM, masonry units were represented as a series of discrete blocks bonded together with zero-thickness interfaces, representing mortar, which can open and close according to the stresses applied on them. Initially, the numerical model has been validated against the experimental data reported in the literature. It was assumed that the bricks would exhibit linear stress-strain behaviour and that opening and slip along the mortar joints would be the predominant failure mechanism. Then, accumulated damage within the seismic response of the masonry walls investigated by means of harmonic load excitations representative of the acceleration time histories recorded during induced seismicity events that occurred in Groningen, the Netherlands.