Although humans have been building impressive, gravity-defying architecture for thousands of years, we still have a limited capacity to quickly and effectively diagnose any developing faults in these structures – something that diminishes our ability to conserve them effectively. In this month’s ‘Science Notes’, we are exploring a simple new technique that seeks to rectify this by clearly determining the flow of forces within stone and brick masonry constructions. Developed by researchers from the University of Sheffield, the new method can be easily applied using basic computer software. It is hoped that that this will help engineers to make quick assessments of the safety of historic cathedrals, bridges, and more, allowing weak structures to be promptly identified and stabilised.
In stone- or brick-built load-bearing constructions – including ones that incorporate elements such as flying buttresses or arches – it is important to understand where the thrust lines are located. A thrust line is the theoretical line where a compressive force passes through the structure. For a structure to be stable, the thrust line must lie entirely inside the masonry. So, as an example, for a stone arch to be stable, all of the force must be contained within the stonework forming the arch; otherwise it will become unstable and collapse.
A method to determine the line of thrust was first proposed by Robert Hooke in the 17th century, and, while it is still widely used, a number of limitations to the technique means that an engineer has to exercise careful judgement when using it – for example, when assessing any structure with openings. The original method is also unable to take into account any possibility of sliding failure, or to identify specific areas of masonry that may be stretched or pulled beyond their limit (that is, beyond their tensile capacity). Although in recent years many attempts have been made to come up with more comprehensive analysis techniques, the methods that have been put forward thus far are generally time-consuming and/or difficult to use in practice.
Enter a new approach, developed by researchers from the Department of Civil and Structural Engineering at the University of Sheffield, called the ‘thrust layout optimisation’ (TLO) method. Building on Hooke’s original model, this new technique uses layout, or topology, optimisation techniques (which are already frequently used in other areas of engineering – for example, to identify tensile and compressive force paths within deep beams or other load-bearing elements). By combining layout optimisation with transmissible loads, compressive force paths can be identified in masonry constructions of any geometry.
Using the new method, not only can the point at which collapse is likely to occur be identified, but the internal distribution of forces within the structure can also be quickly and effectively visualised, something that other techniques have, so far, not been able to do. The method eliminates the need for assumptions to be made by the engineer and means that the process can potentially be used by many different people within the building heritage sector.
The potential significance of the new method was emphasised by Professor Matthew Gilbert, one of the co-authors of the study, who said: ‘Stone and brick masonry has been used for millennia to form buildings and bridges ranging in scale from humble dwelling houses to cathedrals and railway viaducts. Many of these structures have considerable historic value, and, to ensure they remain safe and fit for purpose, effective assessment methods are required.’
The TLO method comes shortly after publication of new government-funded guidance on masonry arch bridge assessment, published by the Construction Industry Research and Information Association (CIRIA) – which provides an important update that, it is hoped, will help preserve historic bridges as they are increasingly having to cope with higher loading than they were intended to carry. The Python script used to generate results in the new work is now available as open-access software too, which, with further development, should be usable by a wide range of people working in heritage conservation – helping preserve our historic structures well into the future.
The full paper outlining the method was recently published in Proceedings of the Royal Society A, and can be read for free here: https://doi.org/10.1098/rspa.2023.0053.
Text: Kathryn Krakowka