The back analysis or inverse analysis of the field instrumentation data is a common technique to ascertain the design parameter validity in deep excavation projects. That analysis is a process full of uncertainties and relies greatly on the expert judgement. Furthermore, deep excavation geotechnical models tend to be computationally very expensive making the inverse analysis a very lengthy process. In this paper, a Bayesian-type methodology to solve inverse problems which relies on the reduction of the numerical cost of the forward simulation through stochastic spectral surrogate models is presented. The proposed methodology is validated with three calibration examples.