Finite element modelling of contact in rubble stone masonry

Multi-wythe masonry walls are a common structural component of heritage buildings. Typically constructed with two dressed outer wythes and a rubble core, these structures are susceptible to environmental degradation, as infiltration of water coupled with freeze-thaw action can break down the existing mortar which can then be flushed out of the wall. The resulting un-bonded core material applies pressure on the outer wythes, leading to lateral displacements and possible failure of the walls. Study of these deformations, and the effects of potential intervention methods through finite element modelling, can ensure adequate measures are selected and implemented. With the core being composed of rounded or fragmented stones and containing little of the original mortar, failure is dominated by rotation and sliding of the stones, rather than failure of the stone units. A dynamic simplified micromodel captures the geometry of the individual stones within a cross-section of a wall from the Prince of Wales fort in northern Canada, allowing translation of the units under self-weight. Linear elastic material properties and frictional contact conditions reduce the complexity of the model while adequately representing the observed conditions. As mesh density is known to impact the results of contact problems greatly, a small sample of stones from the wall has been studied using 8 models containing between 778 and 11701 linear elements. High mesh densities are required to approximate the curved geometry, and reduce faceting due to the flat element edges. These models are run under two separate time steps, in the first the load is applied and in the second the parts are allowed time to reach equilibrium. The resulting displacements of the small models have been examined and compared, optimizing the mesh density for the given sample, which can then be applied to the full cross section.