Optimising embodied carbon and U-value in load bearing walls: A mathematical bi-objective mixed integer programming approach

The construction and building industry is known to be a carbon intensive sector. Of the various opportunities present for minimising the carbon footprint of buildings, optimising the material selection of building components is one plausible avenue for significant carbon reductions. In the construction of opaque load-bearing walls, the thermal performance of the construction build up is the parameter that has the greatest influence over building operational carbon emissions, with thicker profile walls leading to lower U-values and hence lower operational carbon from heating and cooling. Conversely, the extra wall material contributes to increased embodied carbon. The aim of this study is to capture such trade-off between embodied carbon and U-value by presenting a practical optimisation model to design load bearing walls in commercial and residential buildings. In particular, two objective functions are incorporated within the proposed model for the structural design and material selection of the wall layers; the first objective minimises the embodied carbon of the wall while the other minimises the U-value of the wall. The variables forming the optimisation model include the thickness of each wall layer, and the choice of material forming each layer. The proposed model is tested on a practical case example applicable in Australia and the UK, involving a load bearing wall. Results are reported in the form of a Pareto efficient frontier. Utilising the model enables the realisation of the impacts of material selection and wall layering on embodied carbon and U-value of the building structure.