How to model thick thermo-poro-elastic inclusions

Volcanic regions can be characterised by different unrest phenomena and secondary volcanism. Several studies link these phenomena to both magma and hydrothermal fluids. For instance, in the case of the widely studied Campi Flegrei caldera, recent literature suggests that thermo-poro-elastic (TPE) inclusion models are suitable to describe both the observed deformation and seismicity that often accompany its unrest episodes. Some recent works propose analytical solutions to model the case of a thin disc-shaped inclusion, i.e. with a thickness much smaller than its radius. As this restriction may be critical, TPE inclusion models were subsequently extended to cylindrical-shaped inclusions, with an arbitrary thickness, by representing them as a superposition of several thin disc-shaped inclusions (elements). In this paper, we demonstrate how to estimate the minimum number of elements to represent both displacement and stress fields caused by cylindrical TPE inclusions with an arbitrary aspect-ratio (thickness over radius). For aspect ratios greater than 0.3, a single element model will no longer prove suitable to represent both displacement and stress with a good accuracy.