A coupled hydro–mechanical–chemical–biological model for microbially induced calcite precipitation in soils

Microbially induced calcite precipitation (MICP) is a promising ground improvement technique involving complex coupling between hydraulic, mechanical, chemical, and biological processes. However, many existing models focus on selected processes or treat key couplings, such as precipitation-induced stress, in a phenomenological manner, while the role of attached biomass is often insufficiently represented. This paper develops a thermodynamically consistent hydro-mechanical-chemical-biological framework for MICP in soils. Within the framework of non-equilibrium thermodynamics, the entropy production associated with all irreversible processes, i.e., transport, reaction, bacterial attachment, and biomass decay, is quantified and the Helmholtz free energy of the reacting porous medium is rigorously derived. The constitutive relations for stress and porosity are derived from the free energy evolution and expressed in a fully coupled manner, incorporating the hydro-mechanical effects and the contributions of precipitated calcium carbonate and attached biomass to the mechanical response. The resulting governing equations are verified against published numerical results and further applied to two column experiments from the literature. The modelling results show good agreement with experimental observations and reveal that bacterial attachment contributes less than 2% to the overall porosity reduction under typical injection conditions. The proposed framework provides a unified basis for analysing the coupled multiphysics behaviour of MICP-treated soils.