Diffusion-controlled and creep-mitigated asr damage via microplane model. I: Mass concrete

A diffusion-based and creep-based chemo-mechanical model for calculating the evolution of damage caused in concrete and concrete structures by the alkali-silica reaction (ASR) is developed. First the model of Bažant and Steffens for the diffusion controlled kinetics of ASR is reviewed and used to calculate the rate of production of the ASR gel within the aggregate. The next step is the formulation of a nonlinear diffusion model for the penetration of gel into the micropores and nanopores in a mineral aggregate grain, into the interface transition zone (ITZ) and into the nearby microcracks created in the cement paste of mortar. The gel that penetrates the pores and cracks in cement paste is considered to calcify promptly and stop expanding. A novel point, crucial for unconditional numerical stability of time step algorithm, is that the diffusion analysis is converted to calculating the pressure relaxation at constant gel mass during each time step, with sudden jumps between the steps. The gel expansion in the aggregate and the ITZ causes fracturing damage in the surrounding concrete, which is analyzed by microplane model M7, into which the aging creep of a broad retardation spectrum is incorporated. The gel and the damaged concrete are macroscopically treated as a two-phase (solid-fluid) medium of nonstandard type because of load-bearing but mobile water in nanopores. The condition of equilibrium between the phases is what mathematically introduces the fracture-producing load into the concrete. Depending on the stress tensor in the solid phase, the cracking damage is oriented and the expansion is directional. The creep is found to have a major mitigating effect on multidecade evolution of ASR damage, and is important even for interpreting laboratory experiments. Validation and calibration by experimental data from the literature is relegated to Part II.