We consider the task of active exploration of large subterranean environments with a ground mobile robot. Our goal is to autonomously explore a large unknown area and to obtain an accurate coverage and localization of objects of interest (artifacts). The exploration is constrained by the restricted operation time in rescue scenarios, as well as a hard rough terrain. To this end, we introduce a novel optimization strategy that respects these constraints by maximizing the environment coverage by onboard sensors while producing feasible trajectories with the help of a learned robot-terrain interaction model. The approach is evaluated in diverse subterranean simulated environments, showing the viability of traversability-aware exploration in challenging scenarios. In addition, we demonstrate that the local trajectory optimization improves global coverage of an environment as well as the overall object detection results.