## 5 Conclusions  
Based on the analysis of the paste and mortar margins of test samples for the Rich-Mix CSGR material, the following conclusions can be drawn:  
1. The optimum range of paste and mortar margins (\(\alpha\) and \(\beta\)) are 1.05-1.09 and 1.15-1.25, respectively, fill the voids in the fine and coarse aggregates with a surplus for workability margin, providing better enhancement of compressive strength development in CSGRD projects when the rich-mix C\({}_{180}\)20 strength class of CSGR for aggregates of apparent density \(\geq\) 2450 kg/m\({}^{3}\) needs to be achieved reliably, quickly, and economically. 2. The significance of the paste margin on the compressive strength development implies that paste margin is a critical factor in determining the compressive strength of rich-mix CSGR; therefore, cementitious content \(\geq\) 80 kg/m\({}^{3}\) (cement \(\geq\) 40 kg/m\({}^{3}\)) and water/binder should range from 0.7-1.3 need to be considered for parent CSGR, cement slurry of 8-12% addition rate and w/c of 0.5-0.6 for rich mix preparation. 3. The consistent negative correlations and significant \(p\)-values across nearly all curing periods suggest that an uncontrollable mortar margin has a detrimental effect on the compressive strength development of CSGR, which is powerful at 28 days and persists through 180 days. The data imply that a higher mortar margin could lead to weaker CSGR, making controlling the sand ratio between 18% and 35% crucial. 4. The \(\alpha\) and \(\beta\) values approached their optimum as the VC value decreased significantly, enhancing workability. Notably, a VC value of 2 to 8 s was associated with rapid and high compressive strength development towards the C\({}_{180}\)20 strength class and warrants further study and application in future projects. 5. The aggregate type, fine content, type of cementitious materials, type and extent of curing, and others play vital roles in the compressive strength development of CSGR,in addition to the critical roles of paste and mortar margins. Researchers must refer to the technical guidelines for cemented granular materials (SL678-2014) [14]. Further studies on the effects of mud content, fine content, admixture content, and sand ratio are ongoing to analyze and understand how material properties impact the performance of CSGR, specifically on Rich-Mix and Grout-Enriched Vibrated CSGR in CSGRD applications, aiming to establish criteria for performance enhancement. Formal analysis and investigation, [PERSON] ([PERSON]) and W.A.B. ; methodology, W.A.B. ; resources, B.J. ; writing--original draft, W.A.B. ; writing--review and editing, W.A.B., J.J. and Y.W. ([PERSON]); supervision, [PERSON], C.Z. and Y.W. ([PERSON]); funding acquisition, J.J. All authors have read and agreed to the published version of the manuscript. This research is financially supported by the National Key Research and Development Plan of China under Grant No. 2018 YFC0406801. All relevant data are included in the paper. This study was supported by the State Key Laboratory of Simulation and Regulation of Water Cycles in River Basins. The authors declare no conflicts of interest. The following abbreviations are used in the manuscript \begin{tabular}{l l} CSGR & Cemented Sand, Gravel, and Rock \\ CSGRD & Cemented Sand, Gravel, and Rock Dam \\ CMD & Cemented Material Dam \\ \(\alpha\) & Paste Margin Value \\ \(\beta\) & Mortar Margin Value \\ C\({}_{180}\)20 & Rich-Mix (High-Cemertitious) CSGR with Compressive Strength of 20 MPa at 180 days \\ SL678-2014 & Technical Guideline for Cemented Granular Materials issued by the Ministry \\ VC & Vibrating-Compacted Value \\ CSG & Cemented Sand and Gravel \\ RCC & Roller Compacted Concrete \\ HCRCC & High-Cemertitious Roller Compacted Concrete \\ SHCRCC & Super-High-Cemertitious Roller Compacted Concrete \\ MSA & Maximum Size of Aggregate \\ CVC & Conventional Vibrated Concrete \\ ICOLD & International Committee on Large Dams \\ USACE & United States Army Corps of Engineers \\ USBR & United States Bureau of Reclamation \\ \end{tabular}