Geotechnical reservoirs and repositories in salt such as nuclear waste disposals, geothermal systems, and Compressed Air Energy Storage (CAES) are usually subject to complex thermo-mechanical conditions, leading to crack initiation, propagation, and rebonding. This work aims to model thermomechanical damage and healing around salt caverns, by enriching the framework of continuum damage mechanics with fabric descriptors. In order to infer the form of fabric tensors from microstructure observations, we carry out creep tests on granular salt under constant stress and humidity conditions. We simulate a stress path typical of CAES conditions at the material element level. The model presented in this paper is expected to improve the fundamental understanding of damage and healing in rocks at both macroscopic and microscopic levels, and the long-term evaluation of geological storage facilities.