## 2 Materials and Methods
### Material Properties
#### 2.1.1 Grading, Shape and Texture  
The particle- and mode-size distribution curves for the F161 sand, as determined from dry sieving in compliance with BS1377-2 [26], are presented in Figure 1, with the material's deduced gradation parameters summarized in Table 1. F161 sand is a bimodal, moderately-well sorted fine sand, with \(D_{50}\) = 0.23 mm. In Figure 1b, the first and second pronounced modes for F161 sand are 0.24 and 0.50 mm, respectively. The minimum and maximum void ratio (\(e_{\text{min}}\), \(e_{\text{max}}\)) measured in accordance with ASTM D4253 and D4254 were 0.548 and 0.943, respectively. The gradation properties of the NS material were provided by the manufacturer, ISATIS Group, with its \(D_{50}\) range reported as 11-16 nm. Figure 2 shows the shape and texture of the sand grains and precipitated hydrosols, as evidenced from secondary electron-microscopy images. To clear the sand from organic matters and carbonates, it was first treated with 0.5 N (Normality) HCl solution (150 mL acid diluted with distilled water to produce a total volume of 800 mL), then thoroughly washed with distilled water and treated with a 35 wt.% H\({}_{2}\)O\({}_{2}\) solution. Next, the sand grains were washed with distilled water, dried at 40 \({}^{\circ}\)C for 24 h and a random subset of them chosen for microscopy analysis. Figure 1: Grading quality for F161 sand: (**a**) particle size distribution; (**b**) mode size distribution. Figure 2: Shape on secondary electron micrograms: (**a**) sub-angular F161 sand particles; (**b**) rounded hydrated amorphous NS flocs. Particle shape was quantified in terms of sphericity and roundness, employing the methods introduced in [PERSON] [27]. Sphericity (\(S\)) is a measure of convergence of the particle dimensions in the three-dimensional coordinate system, and can be estimated as a function of \(r_{max-in}\), the radius of the largest sphere inscribing the particle, and also \(r_{min-cir}\), the radius of the smallest sphere circumscribing the particle:  
\[S=\frac{r_{max-in}}{r_{min-cir}} \tag{1}\]  
Particles with highest sphericity (i.e., approaching unity) contain minimum eccentricity and platiness. Roundness (\(R\)), a measure of surface features and scale relative to the particle radius, can be estimated as a function of the equivalent particle radius (\(r_{i}\)), the average radius of surficial features, and \(N\), the number of surficial features:  
\[R=\frac{\sum\frac{r_{i}}{N}}{r_{max-in}} \tag{2}\]  
Angular particles have the minimum roundness index. The shape parameters for the F161 sand and precipitated hydrosolocs (i.e., hydrated amorphous silica) are listed in Tables 1 and 2. The roundness and sphericity of F161 sand is much lower than that of the NS flocs. The roundness implies quick precipitation of silica and that colloidal NS particles probably polymerize in the pore-void solution and then settle (at constrictions between neighboring sand grains) in the form of coagulated porous hydrated gel. The adjustments adopted for, and the implications of, the imposed quick precipitation rate are further discussed later in the paper. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(R\) & 0.428 \\ \(S\) & 0.604 \\ \(D_{10}\): mm & 0.16 \\ \(D_{30}\): mm & 0.21 \\ \(D_{50}\): mm & 0.23 \\ \(D_{60}\): mm & 0.28 \\ \(C_{\text{u}}\)\({}^{\ddagger}\) & 0.97 \\ \(C_{\text{c}}\)\({}^{\ddagger}\) & 1.78 \\ \(G_{\text{s}}\) & 2.68 \\ \(\epsilon_{\text{min}}\) & 0.548 \\ \(\epsilon_{\text{max}}\) & 0.943 \\ \hline \hline \end{tabular} \({}^{\ddagger}\) coefficient of uniformity; \({}^{\ddagger}\) coefficient of curvature.  
\end{table} 
Table 1: Grading, packing and shape parameters for F161 sand.