Collimation is essential in a high Energy and Intensity hadron collider with SuperConducting magnets, like the LHC at CERN. To improve the cleaning efficiency and to reduce the LHC impedance budget in stable condition and at top Energy, additional 30 Phase II collimators are foreseen to be installed. The work of this PhD analyses the beam-machine interactions in the LHC Betatron Cleaning Insertions for its upgrade with the Phase II collimators. These studies aim at optimizing the collimation system layout from the machine protection point of view, considering different options for the Phase II collimator design and focusing on heating damage and activation problems. The outcomes of this PhD work have been used to support the Phase II design evolution and their prototype mechanical integration, and to point out possible critical points along the Betatron Cleaning Straight Section. Emphasis is on studying several configurations and material choices for nominal and failure scenarios.