Developed in the late 1980s, Nonlinear Resonant Ultrasound Spectroscopy (NRUS) has been widely employed in the field of material characterization. Most of the studies assume the measured amplitude to be proportional to the strain amplitude which drives nonlinear phenomena. In 1D resonant bar experiments, the configuration for which NRUS was initially developed, this assumption holds. However, it is not true for samples of general shape which exhibit several resonance mode shapes. This paper proposes a methodology based on linear resonant ultrasound spectroscopy, numerical simulations and nonlinear resonant ultrasound spectroscopy to provide quantitative values of nonlinear elastic moduli taking into account the 3D nature of the samples. In the context of license renewal in the field of nuclear energy, this study aims at providing some quantitative information related to the degree of micro-cracking of concrete and cement based materials in the presence of thermal damage. The resonance based method is validated as regard with concrete microstructure evolution during thermal exposure.