## 2 Research Background  
A crucial process in dam construction is dam material compaction. Compared with similar research in other engineering fields, the compaction measurement indices can mainly be divided into two categories: the physical indices and the mechanical indices [8; 9; 10]. The common indices are summarized in Table 1 according to category. The main indices currently applied in earth-rock dam projects are the physical indices (i.e., the compactness \(K\) and the porosity \(n\)), which are obtained by random spot tests. Additionally, the nondestructive alternatives for physical indices such as nuclear density gauge method and additional mass method have been applied at the construction site [3]. The above detection techniques belong to the point-control and post-control methods. For the point-control method, less than 1% of the entire working face can be assessed [11]. For the post-control method, the time-consuming process will delay construction progress and is inconducive to timely construction feedback control. To get around these obstacles, the RTCM system has been rapidly developed, as it can realize continuous compaction control and evaluation [12], and various real-time prediction methods for physical properties of dam materials have been investigated. For example, based on the compaction parameters (i.e., rolling speed \(N_{s}\), compaction passes \(N_{p}\), vibration state \(N_{v}\) and compaction thickness \(N_{l}\)) and material parameters (i.e., gradation \(M_{\delta}\) and moisture content \(M_{m}\)), [PERSON] et al. [4] established a compactness prediction model to predict material compactness by using the multiple regression method. [PERSON] et al. estimated the compactness using support vector regression with bacterial foraging algorithm (SVR with BFA) [1] and the support vector regression with the chaotic firefly algorithm (SVR with CFA) [13] respectively, which improved the prediction accuracy to a great extent. In recent years, based on the RTCM technology, continuous measurement indices (CMI) were proposed as substitutes for physical indices. By monitoring the drum acceleration using accelerometers and encoders, [PERSON] et al. [14; 15] proposed the compaction meter value (\(CMV\)) which is derived from the amplitudes of drum acceleration and its harmonics. Based on \(CMV\), other indices (i.e., the resonance meter value \(RMV\), oscillometer value \(OMV\) and continuous compaction value \(CCV\)) were proposed [11]. [PERSON] et al. [16; 17] introduced the \(CMV\) into earth-rock dam construction. By establishing the regression relation with compactness and dry density, they presented the compaction value (\(CV\)) and unit compaction energy (\(UCE\)) as compaction quality measurement indices. Other main CMI are listed in Table 1.  
However, the above-mentioned research only takes the physical indices of compacted materials as the ultimate control indices. Although related to the mechanical properties, the physical indices neglect the uncertainty in the internal structure of dam materials [8], moreover, the relationship between physical and mechanical indices is only empirical and lacks a strict theoretical basis [15; 18]. The physical indices can only reflect the physical composition and seepage property and fail to represent the mechanical properties. Additionally, since there is a stronger correlation between the drum vibration acceleration and the material stiffness or modulus [19], it is more appropriate for the drum vibration acceleration to establish a prediction model with the mechanical indices than the physical indices. Therefore, reasonably considering both the properties of dam materials will help fully reflect the compaction quality. Due to its simplicity and flexibility, the analytic hierarchy process (AHP) method, proposed by [PERSON] [20], has been widely used to solve comprehensive evaluation problems [21; 22]. In the method, the weights of the alternatives are given by the decision-making experts.