The selection of a ground motion intensity measure (IM) is an essential criterion for judging the expected intensity level of ground motion in the vulnerability analysis of underground structures, and it is also part and parcel of the resilience-based seismic design of underground structures. Most of the current studies are based on a statistical analysis of numerical simulation results to obtain a specific IM measuring the damage potential of ground motions for an underground structure, and there is a lack of mechanistic studies based on experimental ways. In view of this, a series of large-scale shaking-table tests of an underground structure in soft soils were carried out in this paper to explore the appropriate IMs for measuring the damage potential of ground motions. It is found that the response characteristics of the tested soil-structure interaction (SSI) system gradually become similar to the long-period system as the ground motion intensity increases. The transient fundamental frequency of the tested SSI system moves from the acceleration-sensitive band to the velocity-sensitive band in the ground motion response spectrum. This leads to a decrease in the correlation between the response indicators (RIs) of the system and acceleration-based IMs and an increase in the correlation between RIs and velocity-based IMs as well as displacement-based IMs. Based on the test results, the site fundamental period (Tg) and the boundary periods between the sensitive bands in the bedrock response spectrum (Tc and Td) are proposed as identification indexes for selecting the appropriate IM. One of the three measures, PBA, PBV, and PBD, or a composite measure consisting of two of the three, can be adopted as an appropriate IM for an actual underground structure in soft soils in different cases.