A functional risk curve gives the probability of an undesirable event in function of the value of a critical parameter of a considered physical system. In several applicative situations, this curve is built using phenomenological numerical models which simulate complex physical phenomena. Facing to cpu-time expensive numerical models, we propose to use the Gaussian process regression model to build functional risk curve. An algorithm is given to provide confidence bounds due to this approximation. Two methods of global sensitivity analysis of the model random input parameters on the functional risk curve is also studied. As important information is given by the PLI sensitivity indices which allow to understand the effect of misjudgment on the input parameters' probability density functions.