## 2 Research Background
However, due to complexity in the construction field and the insufficient experience to support the experts to make a fully deterministic judgement, the results are usually subjective and uncertain [22]. To address this problem, several theories have been developed, including the evidence theory, probability theory, fuzzy set theory and convex set theory [23]. Among these theories, the interval model, as a representative of the convex set model, is extensively used since it is easy to combine with on-site statistical data. The model can take the subjectivity and uncertainty into account by extending the deterministic numbers to bounded intervals [24]. Therefore, the mathematical model of AHP extended by the interval model (\(i\)-AHP) method is introduced for the evaluation of real-time compaction quality. Besides, although it is crucial for dam safety, the inherent heterogeneity of dam material compaction has rarely been studied. The reason may be that it cannot be quantified until the RTCM technology is introduced to dam construction which realizes full monitoring coverage of the working face. In other engineering fields, the geostatistical analysis method (GAM) has been introduced to spatial heterogeneity analysis [25; 26]. Based on the GAM, [PERSON] et al. [27] studied the effect of compaction quality heterogeneity on structural response in highway pavements and proposed the _Cova_ index to quantify the heterogeneity. The semivariogram model parameters in these studies are fitted using the least square method or the weighted regression method; however, the fitting accuracy needs to be further discussed. The objectives of this paper are to: (1) establish the prediction models for the physical and mechanical indices of earth-rock dam materials; (2) based on the \(i\)-AHP method, establish a hybrid evaluation model for real-time compaction quality, which considers both physical and mechanical properties and deals with the uncertainty in determining the weights of the alternatives, and to develop the hybrid compaction index (\(HCI\)); and (3) present the improved GAM (\(i\)-GAM) to improve the model fitting precision and investigate the inherent heterogeneity of the \(HCI\). Through the above work, the comprehensive compaction quality evaluation with full coverage can be achieved, and the inherent heterogeneity analysis of compaction quality can help find the weak construction area which is benefit for timely feedback control. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Categories** & **Indices** & **Symbols** & **Detection Methods** & **CMI** & **References** \\ \hline \hline \multirow{3}{*}{Physical properties} & Compactness & \(K\) & Spot tests & & IWHR [3] \\  & Poorly & \(n\) & Spot tests & & IWHR [3] \\  & Dry density & \(\rho_{d}\) & Spot tests & & IWHR [3] \\ \hline \multirow{3}{*}{Mechanical properties} & Dynamic elastic modulus & \(E_{d}\) & Light weight deflectometer (LWD) tests & & [PERSON] et al. [28] \\  & Deformation modulus & \(E_{0}\) & Plate load (PL) tests & & [PERSON] et al. [29] \\  & Subgrade modulus & \(K_{00}\) & PL tests & & [PERSON] et al. [29] \\  & California bearing ratio & CBR & Dynamic cone penetrometer tests & & [PERSON] et al. [28] \\ \hline \multirow{3}{*}{Nondestructive alternatives} & Density & \(\rho\) & Nuclear density Gauge tests & & IWHR [3] \\  & Density & \(\rho\) & Additional mass tests & & IWHR [3] \\  & Compact metric value & CMV & KICM technology & \(\surd\) & [PERSON] et al. [4] \\  & Compaction value & \(CV\) & KICM technology & \(\surd\) & [PERSON] et al. [16] \\  & Unit compaction energy & \(UEC\) & KICM technology & \(\surd\) & [PERSON] et al. [17] \\  & Sound compaction value & \(SCV\) & KICM technology & \(\surd\) & [PERSON] et al. [5] \\  & Machine drive power & MDP & KICM technology & \(\surd\) & [PERSON] et al. [30] \\  & Bonus variacontrol & \(BVC\) & KICM technology & \(\surd\) & [PERSON] et al. [31] \\  & Sol stiffness & \(k_{b}\) & KICM technology & \(\surd\) & [PERSON] et al. [23,33] \\ \hline \end{tabular}
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