The sustainability of geotechnical infrastructures is closely linked with their long-time behavior. In fact, there is not a straightforward procedure to predict this behavior, and very often, the back analyses of observed data are the best tool to understand their long-time response. In-situ observations of drifts constructed in the Callovo-Oxfordian (COx) claystone, the potential host formation for geological radioactive waste disposal, in France exhibit a progressive convergence. These convergence measurements with quite significant dispersions reveal a considerable uncertainty of time-dependent behavior of this argillaceous rock that can strongly affect the transmit loading to liners, hence the long term stability of the drift. Consequently, the uncertain quantification of the creep behavior of COx claystone presents an important task before analyzing the safety of the waste disposal system. In this work, this challenge was conducted by using the well-known Bayesian inference technique. For this aim, on the one hand, the effectiveness of the classical and hierarchical Bayesian techniques to quantify the epistemic and aleatoric uncertainties of the time-dependent behavior of the host rock were investigated using synthetic data. On the other hand, we dealt with the uncertain quantification of the Lemaitre parameters that characterize the visco-plastic behavior of COx claystone thanks to the real data of in-situ convergence measurements of drifts.