# Geomechanical analysis of the stability conditions of shallow cavities for Compressed Air Energy Storage (CAES) applications

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## Abstract

Compressed Air Energy Storage (CAES) systems compress air into underground cavities when there is an excess of energy production (e.g., in the electrical grid or in an electrical plant) and generate electrical energy using a turbine when the electricity demand exceeds the production. Underground air storage requires construction of new underground cavities or reconditioning of existing underground openings. This paper presents a study of geomechanical stability of shallow circular cavities carried out as part of a multidisciplinary project that investigated the feasibility of using existing underground mining works (drifts and shafts) from iron mining works dating back from the first half of the twentieth century in northern Minnesota (USA). The paper addresses the fundamental problem of establishing the stability conditions of shallow cylindrical or spherical openings excavated in cohesive ground, and subjected to either decreasing or increasing internal pressure, associated with the process of contraction or expansion of the cavities during operation of a CAES system. A statically admissible analytical model for a shallow circular opening in cohesive ground derived from the limit analysis lower bound theorem is presented, and key dimensionless groups of variables controlling the stability of the cavity, defined in terms of a scalar factor of safety, are identified. The analytical model allows several observations of practical interest to be made with regard to the stability of shallow cavities. Numerical finite-difference models are used to validate the various observations and to quantify the underestimation of factors of safety obtained with the proposed lower bound solution. The paper also presents a critical evaluation of limit equilibrium (Terzaghi’s type) models that are traditionally used to design cavities for gas and air storage. Comparisons of results obtained with existing limit equilibrium models, with the proposed analytical model and with numerical models, show that limit equilibrium models can lead to both over conservative (i.e., too safe or uneconomical) and to nonconservative (i.e., unsafe) cavity designs depending on the ranges of values considered for the dimensionless groups of variables governing the problem. Finally, the effect of various parameters such as water in the ground, frictional strength and others, on the stability of the cavity are discussed.

### Keywords

CAES Shallow cavities Stability Factor of safety Limit analysis Limit equilibrium### References

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