Lucas-Washburn vs Richards equation for the modelling of water absorption in cementitious materials

Abstract

The Lucas-Washburn equation is still being applied by a significant number of researchers for the modelling of water absorption in cementitious materials. A modern approach considers the extended Darcy’s law leading to the Richards equation instead. Three main assumptions are implied by the application of the Lucas-Washburn equation: the flow occurs in one direction only, the material is separated into one fully wet and one fully dry region, and pores are modelled as an assembly of parallel tubes of a particular radius. Its application to analyse experimental results allows defining these three assumptions as mere simplifications. Therefore, all the parameters comprised in the Lucas-Washburn model are apparent. Consequently, a very limited description of the transport properties of the material can be achieved. For many engineering purposes this would not be an issue, but for an intrinsic description of the material a more realistic model is required. This paper discusses the limitations of the Lucas-Washburn equation, and the advantages of the Richards equation regarding the modelling of water absorption in cementitious materials. The comparative analysis reveals the versatility of the Richards equation, with an approach that considers the material as a continuum and describes it through measurable parameters.