An improved mathematical model for predicting degradation of building materials

Abstract

Recently an extremely simple but fairly good model that defines the rate of degradation of building materials was suggested. The mentioned differential equation defines a degree of degradation as time dependent function under the assumptions that both conditions external (from the environment) and internal (inside the material) remain constant. This paper offers an improvement by taking the factor, which represents a response of the material to the aggression, as time-dependent function. It was proved that the simplest form (an ordinary linear function) satisfies the expectations. Adequateness of the improved model was confirmed by the following examples: reduction of both weight and mechanical characteristics of degraded concrete, bonding of aggressive sulphate ions to cement constituents, degradation of blasted- steel panels and cracking of concrete due to hydration. The conclusions were drawn by comparison of the improved model, on the one hand, and the original model and power law model, on the other hand. For comparison, a few statistical parameters (such as χ2, correlation coefficient and confidence interval for parameters) were used.