Energy-based identification of characteristic stresses in weakly cemented rocks during stepwise cyclic loading–unloading

Weakly cemented rocks, characterized by poor cementation, loose internal structures, and well-developed pore networks, exhibit pronounced heterogeneous deformation. This heterogeneity limits the applicability of conventional methods for identifying characteristic stresses based on strain, acoustic emission, or wave velocity. In this study, stepwise cyclic loading–unloading tests were conducted on argillaceous siltstone, a representative weakly cemented rock. The partitioning and transformation of energy during the loading–unloading process were systematically analyzed. By accounting for stress–strain asynchrony, elastic energy and dissipated energy were rigorously separated, and elastic energy was further decomposed into particle elastic energy and crack elastic energy. A quantitative method for determining characteristic stresses was proposed based on the ratios of particle elastic energy and crack elastic energy, along with the increment of dissipated energy. The closure stress ( σ cc ), crack initiation stress ( σ ci ), and damage stress ( σ cd ) were determined by the energy-based method. Independent validation using the evolution of the dilatancy point and the acoustic emission hit count demonstrated strong consistency with the proposed energy-based method. By using the complete dataset obtained from stepwise cyclic loading–unloading tests and avoiding subjective interpolation or manual point selection, this approach provides a robust framework for accurately determining characteristic stresses in weakly cemented rocks.