The verification of properties on a Time Petri net is often based on the state class graph. For a highly concurrent system, the construction of a state graph often faces to the problem of combinatory explosion. This problem is due to the systematic interleaving of concurrent transitions. This paper proposes a new method of unfolding limiting as much as possible interleavings. This unfolding keeps a partial order execution and interleaving are hold on when their allow to put all conflicts in a total order. The method gives a way to generate a complete finite prefix unfolding based on the construction of the exhaustive set of scenarios on a safe time Petri net. Moreover, the method allows various quantitative time analyses based on the complete finite prefix unfolding and on a permanent time database.