## 1 Introduction  
To promote the benign development of the global ecological environment, governments have made great efforts to develop clean energy. In this context, pumped storage projects, as one of the most mature energy storage methods, have been rapidly developed and constructed. Rockfill dams are extensively utilized in the context of pumped storage projects, primarily due to their cost-effectiveness and high structural reliability. As the construction of rockfill dams accelerates and their height increases, the accurate monitoring of their structural changes and the reasonable determination of safety monitoring indices becomes increasingly imperative. This is essential for ensuring the safe operation of these dams [1,2]. The purpose of determining the monitoring index is to assess and predict the dam's ability to resist possible loads and thus to determine the extreme value (maximum allowable value) and warning value (a certain percentage of extreme value) of the effector under that load combination. The prevailing methods for determining the monitoring index of dam displacement are the confidence interval method [3], the typical small probability method [4], and the structural analysis method [5]. The former two are mathematical statistics methods that utilize probability statistics theory and existing monitoring data to assess the monitoring displacements of dams. They offer the advantage of being simple and easy to operate. However, in dam displacement, monitoring data are less extensive and are not obtained through the most unfavorable loading conditions; the monitoring indexes determined through the two methods do not depict the extreme value of the real state. In addition, the physical concepts of the monitoring indexes based on mathematical and statistical methods are not clear because they are not related to the mechanical characteristics and deformation mechanisms of the dam structure. The structural analysis method adopts the finite unit method to establish a model to simulate the force characteristics of the dam, and the physical concept is clear, so it can calculate the deformation and stress change of the dam body under various working conditions and then simulate certain loading conditions that have never been encountered, which is more suitable for determining the monitoring index of the safety of the whole life cycle of the dam [6; 7; 8; 9]. In the conventional monitoring index determination based on the structural analysis method, it is generally accepted that the mechanical parameters of the rockfill material are determined. That is to say that the parameters of the laboratory geotechnical test are used for the structural calculations and, consequently, for the determination of the water pressure component [10]. However, in actual project implementation, influenced by factors such as geological investigation, geotechnical test, design assumptions, construction technology, and construction conditions, significant variations in the rockfill materials are evident. These variations encompass the physical properties of the rockfill materials (density, pore ratio, average particle size, etc.) and mechanical parameters. The existence of certain uncertainties and random distribution characteristics has been demonstrated in the extant references [11; 12; 13]. Ignoring these uncertainties in safety monitoring and risk evaluation has been shown to have a serious impact on the deformation prediction and safety analysis of dams, as shown in Table 1, resulting in monitoring index deviation and difficulties in accurately and comprehensively responding to the true operational state of a rockfill dam [14; 15; 16]. To fully consider the impact of the uncertainty of the above parameters on the deformation of the rockfill dam, simulate the displacement changes of the dam body more realistically, and establish reasonable and accurate displacement monitoring indexes for the rockfill dam through structural analysis, this paper proposes a new method for formulating monitoring indexes.