Formulating the Torsion Strength of Dry-stacked Stone Blocks by Comparing Convex and Concave Contact Formulations and Experimental Results

Objectives: The objective of this work is to investigate the reliability of the two formulations most commonly used in modeling the geometric contact of dry-stacked stone blocks, i.e. those based on concave and convex contact assumptions. Methods: A comparison between these two formulations for the yield domains of torsion and torsion-shear interaction is carried out; the analytical results are then compared with experimental outcomes existing in the literature and difference percentages are evaluated in terms of shear forces. For both formulations, the reference model of two dry-stacked rigid blocks is adopted with the hypotheses of infinite compressive strength for blocks, absence of tensile strength and frictional behaviour at their contact. Findings: The analysis underlines that the convex formulation provides more reliable results in terms of both pure torsion and interaction between torsion and shear. In fact, the percentage difference between experimental and analytical shear forces results to be very small in this case, while a great difference is estimated for concave formulation, both for pure torsion and torsion-shear interaction. Then a possible correction of the torsion capacity in the concavity model is proposed assuming a proper reduction of the contact area. This simple criterion allows obtaining a good agreement of the yield domains with those obtained by convexity model and experimental results. With the proposed correction the simplicity of the algorithms of the concave formulation can find interesting applications in rigid block limit analysis, especially for non-associative friction solutions of 3D masonry block assemblages, thanks to the very low computational effort compared with all the other existing solution procedures. Application/Improvements: Additional experimental work is being carried out to fully validate such correction and to investigate its effect on the torsion-bending moment interaction.