This paper introduces a new formulation of the A-theta integral for a three-dimensional orthotropic medium influenced by a moisture content field. Derived from the generalized Noether theorem, the integral incorporates a moisture content gradient coupled with mechanical fields in both real and virtual configurations. It is extended to account for viscoelastic behavior through a fractional rheological model, enabling the evaluation of the energy release rate during crack propagation. The proposed integral also facilitates the decoupling of mixed crack modes under complex loading conditions and is adapted for crack growth in orthotropic viscoelastic media by introducing a pressure component at the crack surfaces. Independence of the integration path is verified. Additionally, the integral is implemented in the finite element software Castem, coupled with an incremental viscoelastic process. Numerical results demonstrate the impact of the moisture content field on energy release rates and are compared with experimental findings.