Statistical damage constitutive model of MICP-treated specimens based on lognormal distribution

Microbial-induced carbonate precipitation (MICP) technique has the potential to be an eco-friendly and sustainable solution for engineering problems. Despite the extensive amount of research that has been conducted recently on the MICP technique, there are few studies on the constitutive model of MICP-treated specimens. In this study, the statistical damage constitutive model of MICP-treated specimens was established based on the statistical theory and damage mechanics theory. The proposed model assumed that the microelement strength of biocemented sand follows the lognormal distribution and the Drucker–Prager criterion. The parameters S₀ and F₀ in the constitutive model were determined, and their physical significance was then discussed. The reasonableness of the proposed model was verified by comparing the theoretical results and the experimental results. The evolution of the damage variable (D), parameter S_0, and parameter F₀ with different calcium carbonate content (CCC) was analyzed. The statistical damage model based on the lognormal distribution was then compared with that based on the Weibull distribution. The results show that the parameter F₀ and S₀ can reflect the limiting strength and brittleness of MICP-treated specimens.. The specimens with higher cementation tend to have a higher accelerated damage rate. The damage variables eventually reach a stable value as the axial deformation increases. The proposed model can reflect the strain softening and strain hardening phenomena well, which can also represent the shear expansion and shear contraction characteristics of the volume strain curve. Overall, the research in this study can provide some theoretical support for the engineering application of MICP-treated specimens.