Theoretical solutions for strength-scaled unreinforced masonry for scaled soil-structure experimentation

Reduced-scale masonry testing offers advantages of lower costs and shorter schedules compared to full-scale testing, but achieving results reflective of full-scale behavior requires development and fulfilment of appropriate scaling relationships. In many model-scale experiments, geometric scaling occurs but kinematic and/or dynamic similitude is not fully satisfied. This paper describes the theoretical basis and evolution of the equations necessary to achieve kinematic similitude for soil-structure testing at one-gravity for unreinforced masonry. Critical considerations relate to preventing the soil from being overloaded. By adopting a standard linear relationship of increased soil stiffness with depth, the controlling principle becomes the application of restricted, scaled loads throughout the entirety of the structure-soil system. As such, material strength and stiffness must be scaled accordingly to respond appropriately under the reduced stress. An example is provided for an adjacent excavation experiment with related empirical verification and computational quantification.