Statistical damage constitutive model of MICP-treated specimens based on Lognormal Distribution

Abstract

Microbial-induced carbonate precipitation (MICP) technique have the potential to be an eco-friendly and sustainable solution for engineering problems that has presented promise in various geotechnical applications. Despite the extensive amounts of studies about the MICP technique has been conducted recently, 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 model assumed that the microelement strength of bio-cemented sand obeys the log-normal random distribution and the D-P criterion. The parameters S0 and F0 in the constitutive model were determined and the physical significance of parameters were discussed accordingly. The reasonableness of the proposed model were verified by comparing the theoretical results and the experimental results. The evolution of the damage variable (D), parameter S0 and parameter F0 with different calcium carbonate content (CCC) were analyzed. The statistical damage models based on log-normal distributions was then compared with that based on Weibull distributions. The results show that the parameter F0 and S0 can reflect the limiting strength and brittleness of MICP-treated specimens, respectively. The damage rate accelerates with increase in cementation level, leading to larger damage values. The damage variables eventually reaches 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 provide some theoretical support for the engineering application of MICP-treated specimens.