In this work, we propose a new meta-model to describe the evolution of the degradation of infrastructures for reliability purposes. The model takes into account both hazards, temporal and spatial. It is based on the classical homogenous or non-homogenous Gamma process, the scale parameter is modeled with log-normal random field in order to assess and incorporate the effect of the spatial variability and heterogeneity on the degradation process. Simulation results are performed using synthetic data based on Monte-Carlo simulations to fit the model, the inference of their parameters is performed using the method of moments combined with curve fitting method. Computation and estimation of quantities of interests for reliability or maintenance studies, namely the failure time and remaining life-time are developed and illustrated by numerical examples.