A fictitious Stress-Based model of coal modulus evolution under the influence of gas sorption

• Identifies diverse coal modulus evolution behaviours under gas adsorption. • Embeds fictitious stress into an unconventional effective-stress (UES) framework. • Derives porosity–modulus coupling relationships governed by UES. • Explains weakening, strengthening, and near-invariant modulus trends. • Sensitivity isolates impacts of initial porosities and Langmuir constants. Experimental observations have demonstrated that gas sorption alters coal mechanical properties, such as coal strength and Young’s modulus, during gas injection/extraction under different stresses. According to the Terzaghi effective stress (TES) principle, the evolution of these mechanical properties is a function of the TES. Under this premise, significant discrepancies are observed between experimental observations and TES-based predictions. These discrepancies indicate that the TES framework is insufficient to describe coal mechanical behavior under gas sorption. In this study, the concept of adsorption-induced fictitious stress is introduced to provide an extended definition of effective stress during gas injection and extraction, and the resultant stress is termed the unconventional effective stress (UES). On this basis, the TES principle is reformulated as the UES principle. A UES-based model of coal modulus evolution is derived, validated against four sets of laboratory data reported in literature, and applied to a series of sensitivity studies. Within the proposed framework, adsorption-induced changes in effective stress are identified as the direct driver of the diverse trends in Young’s modulus evolution. The introduced fictitious stress captures the effective-stress variations caused by heterogeneous swelling, thereby defining an upper bound (self-constrained swelling) and a lower bound (self-facilitating swelling) for Young’s modulus evolution, with coal properties regulating the position between these bounds through their control of UES. These results demonstrate that the proposed UES-based model reconciles the discrepancies between experimental observations and theoretical predictions.