Multiple expansion and non-linear breakage mechanism of local micro-fractures in limestone with energy storage and separation under cyclic loading

•The nonlinear characteristics and propagation path of 3D microcrack propagation are systematically analyzed.•The relationship between three-dimensional crack propagation and energy evolution is analyzed.•A nonlinear model of free energy separation is proposed.•Analytical solutions of nonlinear parameters are obtained.•The theoretical curves of nonlinear parameters are in good agreement with the experimental data.•The theoretical curves of nonlinear parameters well reflect the experimental process data.•The theoretical model is consistent with the experimental results. Limestone is a widely used building material, and its deformation and failure process is affected by unloading or other disturbing loads. To explore the progressive propagation law of micro-cracks, energy conversion in the progressive failure and nonlinear breakage mechanism in limestone, 3D acoustic emission experiments are conducted on preloading under cyclic loading and unloading with low frequency and unequal amplitude. The results revealed (1) the 3D evolution characteristics of the microstructure local deformation and breakage under load action are related to the location and number of pre-cracks. (2) The ratio of elastic energy to total energy indirectly reflects the microstructure local deformation and breakage development stage. The ratio of dissipated energy to total energy directly reflects the gradual evolution of microstructure. Energy dissipation is mainly related to the distribution of prefabricated cracks and the location. (3) The research combines calculus in the field of mathematics and thermodynamic principles physics reveals the nonlinear mechanism of the energy evolution process and gives the analytical solution of the nonlinear parameters of Helmholtz free energy separation and the breakage evolution eq. (4) The nonlinear function well reflects the nonlinear characteristics of the limestone degradation process in the experiment; The theory strength and constitutive curve are in good agreement with the experimental results. This research result lays the foundation for the study of more detailed nonlinear breakage theory under different conditions, and makes the integration and development of disciplines closer and deeper.