Modeling the volume oscillation of air masses trapped in deep tunnels

Researchers have extensively studied the behavior of air masses trapped in pipelines and the challenges associated with their impact on system performance. Two theoretical hypotheses primarily guide this research, focusing on pipeline filling and emptying operations. However, adding vertical shafts as regulation and storage elements introduces new dynamics and presents unique application challenges that require updated theoretical frameworks. This study develops a model for the volume oscillation of trapped air masses within a one-dimensional framework by analyzing different formation mechanisms. The morphology and initial pressure head of the trapped air masses influence the impact pressure of the model, a finding that enables future attempts to integrate coupling migration effects. This paper addresses the following aspects of deep tunnel systems with trapped air masses: (1) the deformation motion and trapping mechanisms of air masses under various formation conditions; (2) the selection of water properties for algorithmic modeling without experimental control or fitting; and (3) modeling approaches for multiple air masses using non-concentrated inertia methods. This work provides a reference for analyzing deep regulation and storage tunnel systems impacted by trapped air masses.