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Breakage, Helmholtz free energy, and nonlinearity are involved in many fundamental phenomena of complex systems across natural sciences. However, a mathematical equation that can express the entire life cycle of complex natural objects (such as rock-like quasi-brittle materials) is lacking. We expand the material body system to an isolated compound thermodynamic system to establish an innovative theoretical model induced by coupling nonlinear separation of Helmholtz free energy and breakage evolution that can be used to express the extreme entire life model of rock under unequal amplitude loading and unloading cycle. We gain crucial insights into the life essence of limestone, which is termed "Negative Dissipation." This study first shows that the change in the mechanical properties of quasi-brittle materials caused by the timely evolution of breakage can be represented by the nonlinear separation of Helmholtz free energy and negative dissipation. An analytical solution to the nonlinear separation variables of Helmholtz free energy is provided by combining the method of solving nonlinear partial differential equations in mathematics and thermodynamic law. An analytical solution of Helmholtz free energy considering nonlinearity and breakage is proposed, and an equation that can reflect the constitutive mechanics law of the entire life cycle of rock in the theoretical model is presented. Theoretical results are consistent with the experimental data obtained from limestone samples with different prefabricated cracks. This original study provides a theoretical foundation for the life model of complex natural objects for nonlinear breakage and an early warning investigation of rocks under various unprecedented conditions. This study first found that the change in the mechanical properties of complex natural objects caused by the timely evolution of breakage can be represented by the nonlinear separation of Helmholtz free energy. We establish an innovative theoretical model induced by coupling nonlinear separation of Helmholtz free energy and breakage evolution. The innovative theory includes three parts: (1) an analytical solution to the nonlinear separation variables of Helmholtz free energy, (2) an analytical solution of Helmholtz free energy considering nonlinearity and breakage, and (3) an equation of the theoretical model that can reflect the constitutive mechanics' law of the entire life of quasi-brittle rocks is presented for the first time. This original research result provides the foundation for a more in-depth life cycle of quasi-brittle rocks to develop the theoretical basis for the nonlinear breakage and early warning research of materials under various unprecedented conditions. We report a route to material microstructure composition, which may open an alternative pathway to quasi-brittle materials, which may, in turn, open a door into the mysterious world of science. [ABSTRACT FROM AUTHOR]

The cube is considered the best shape for high-quality ballast aggregates. However, the presence of flaky and elongated aggregates (misshapen particles) caused during ballast production is unavoidable. In this regard, the consequence of using this shape of ballast is not well investigated. In this study, first a series of large-scale direct shear tests were carried out under various vertical stresses of 50, 100, and 200 kPa to evaluate the breakage and level of fines in ballast samples categorized by the flakiness and elongation index. Second, the discrete element method (DEM) was employed to simulate tests concerning the breakage of particles. The results showed that there was a 14.7% and 5.2% decrease in strength and friction angle of aggregates with 20% increase in the percentage of flaky aggregates. An aggregate limit of 25% by weight for misshapen particles is recommended to meet the minimum shear stress level of the flaky ballast sample in the Chinese standard. Despite higher shear strength at low vertical stresses compared with cubic aggregates, flaky and elongated aggregates result in higher deterioration and shorter service life in the long term. [ABSTRACT FROM AUTHOR]