1 A Mathematical Model for the Pessimum Size Effect of ASR in Concrete

ABSTRACT. This study proposes a mathematical model which characterizes the effects of various influential parameters on the pessimum size effect of ASR and predict the development of ASR expansion. The model emphasizes the chemomechanical coupling of the ASR expansion process, the size distribution of aggregates, and microstructural features of cement paste. The mechanical part of the model is developed based on a modified version of the generalized self-consistent theory. The chemical part of the model includes two opposing diffusion processes. One is the diffusion of chemical ions from pore solution into aggregate, and the other one is the permeation of ASR gel from the aggregate surface into the surrounding porous cement matrix. The total ASR gel is divided into two parts: the gel directly deposited in the interface pores which does not cause expansion, and the gel permeated into the surrounding pores in cement paste which generates the interface pressure and is responsible for the expansion. The amount of the first type of gel and the rate of the permeation of the second type of gel depends on the size of the aggregate and the porosity of the cement paste. The balance between the two opposing diffusion processes determines the pessimum size of the aggregate and maximum expansion of the concrete