Using Maxwell’s Theory to model and quantify the fracture evolution of cyclothymic deposition phosphate rock

Abstract

The evolution and stability of fracturing in the cyclothymic deposition of phosphate rocks are strongly affected by the viscoelasticity and structural form of the rock-forming minerals. Presently, there is no standardized method that has been widely accepted to accurately quantify the elastic-plastic deformation and fracturing of such striped structural rock nor reflect the role of the different lithogenous minerals in phosphate rocks when subjected to viscoelastic strain loading. In this study, integrated mathematical equations were formulated for modelling the mechanical and fracture behaviour of cyclothymic deposition in structured phosphate rocks. These constitutive equations were developed based on Maxwell’s Theory after the elastic modulus and damping coefficient of the rock-forming mineral from the mechanical testing were substituted into the derived-equations. In these new models, the apatite stripes and dolomite stripes were incorporated into the transverse isotropic model through the analysis of structural characteristics of the phosphate rock. Through experimental validation, the response curves of the creep and stress relaxation tests were found to be consistent with the deformation curves generated by modelling using the mathematical equations. Overall, the formulated model along with the corresponding equations was found to exhibit good applicability properties to describe phosphate’s mechanical and fracture behaviour under low horizontal compressive stresses. In the study, the creep mechanism in phosphate rocks were satisfactorily analysed from the angles of microscopic morphology, cracks evolution, and inter-crystalline strength. The hard brittle apatite was found to be surrounded and separated by high creep variant dolomite. Furthermore, the analysis showed that dolomite crystals possessing high creep properties dominated the distribution and evolution of secondary structures in the phosphate rock, under the condition of long-term low-stress loading.