Modified linear superposition method for stress tensor field analysis and its application to compressed air energy storage chamber group

Burial depth and spacing are key factors influencing the stability of compressed air energy storage chamber groups. However, methods for determining safe burial depth and spacing in aligned multi-chamber systems remain underexplored. This study introduces a modified linear superposition method (M-LSM) for calculating elastic stress tensor fields in the surrounding rock around multiple chambers. The method analyzes the distribution of elastic stress under varying design parameters and surrounding rock conditions, identifying the most critical stress locations, which are the sidewalls affected by adjacent chambers, and providing deeper insights into stress concentrations caused by chamber interactions. The relationship between safe burial depth and spacing follows an approximately inverse proportionality, with the safety criterion of no plastic zones developing in the surrounding rock. A closed-form solution for safe burial depth and spacing is derived, which can be used to quickly determine the design parameters. The M-LSM is applicable to a wide range of internal pressurized chamber groups and borehole problems, capturing mutual interactions between adjacent chambers more realistically. Compared to finite element method simulations based on a practical engineering case, the results show errors that are typically negligible, validating the reliability of the analytical approach. This fully analytical method is mesh-free, iteration-free, and offers infinite resolution, making it highly efficient for both computations and practical applications. The closed-form solution derived from this method provides significant value for trend analysis, practical calculations, and engineering applications.