This work tackles the open pit planning problem in an optimal control framework. We study the optimality conditions for the so-called continuous formulation using Pontryagin's Maximum Principle, and introduce a new, semi-continuous formulation that can handle the optimization of a two-dimensional mine profile. Numerical simulations are provided for several test cases, including global optimization for the one-dimensional final open pit, and first results for the two-dimensional sequential open pit. Theses indicate a good consistency between the different approaches, and with the theoretical optimality conditions.