## 2 Materials and Methods
### Isotropic Consolidation and Undrained Compression Testing
#### 2.3.1 Variation of Packing with NS Content  
The post-consolidation void ratio and relative density are reflections of the specimen packing state and flow potential of the various binary mixtures. In Graton and Fraser packing system and three-dimensional (3D) Euclidean space, all specimens investigated possess a loose 600 body-centered cubic packing (i.e., each unit cell comprising of 6 square sides) to fairly loose 402 packing (i.e., each unit cell comprising of 4 square sides and 2 rhombohedra sides) state [32]. There is a relatively short route between the 600 and 402 packing states, which essentially encompasses typical collapse through hydro-consolidation or application of modest stress for any granular metastable form (dune sand and loess, and here extended to medium dense sand) from initial void ratios as high as 0.9 to a value of approx. 0.6 [33]. This implies a fairly large collapse potential remains for the sand specimen's post-treatment, a common case in remediation of problematic soils when a proppant is very slowly flushed into the soil's open pore-network. In the next few sections, the extent of this'residual' flow potential is measured and discussed in form of scale-dependent events. For both base and treated sand specimens, Figure 4 presents the variation of the post-consolidation void ratio (\(e_{\text{c}}\)) with mean initial effective stress (\(p^{\prime}{}_{\text{c}}\)) for the four levels of isotropic consolidation pressure investigated. From Figure 4, it is evident that for \(p^{\prime}{}_{\text{c}}=100\) kPa, the variation in NS content over the 0-15% range produced the sharpest drop in the void ratio, demonstrating the pronounced role of silica flocs in facilitating the consolidation; i.e., the higher the fines content, the lower the post-consolidation void ratio and the denser the packing state (higher \(D_{\text{r}}\)). This marks the transition from the 600 and 402 packing state through sand particles' contact modification. For \(p^{\prime}{}_{\text{c}}=200\) kPa, the variation in NS content over the 0-15% range produced marginal changes in post-consolidation void ratio--that is, \(\varepsilon_{v}=(e_{\text{S(0):100}}-e_{\text{S(15):100}})/\big{(}1+e_{\text{S (0):100}}\big{)}=0.56\%\). This marks a packing state where the direct interlocking between sand grains diminishes the impact of silica flocs in consolidation volumetric change. As the effective stress increases beyond 200 kPa, only a modest rise in the \(\varepsilon_{v}\) was recorded with increasing NS content. This suggests that silica flocs regain control on the packing state during consolidation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test ID** & \(p^{\prime}{}_{\text{c}}\)** **kPa** & **NS: wt.\%** & \(e_{\text{c}}\) & \(D_{\text{r}}\)** **\%** \\ \hline S(0):100 & 100 & 0 & 0.808 & 34 \\ S(1):100 & 100 & 1 & 0  
Overall, the compressibility increases with NS content and \(p^{\prime}c\), and does not appear to decrease as specimens become denser. The latter marks a fundamental difference between sand-silt composites and sand-NS composites. Using the Mai Liao silty fine sand deposits in western Taiwan as an example, the fines content can vary from 0% to 50% and compressibility decreases with increasing fines content because it produces denser specimens. In the present investigation, the air-pluviation method employed in preparing the test specimens led to the formation of an initial open packing. Polymerized NS flocs tend to accumulate at grain contact points. Flocs form interparticle bridge and buttress units, shield the sharp particle asperities and enhance the apparent cohesion (elaborated in following sections). For low initial mean effective stresses (100 kPa), interparticle silica flocs benefit from lower confinement levels and facilitate the rearrangement of sand particles. At 200-kPa effective stress, rearranged sand particles directly engage with one another through interlocking.