## 3 Undrained Shear Behavior for Binary Mixtures
These volatilities could indicate a period of rapid interactions between the sand particles and rounded NS floc units, suggesting particle rearrangement and, as such, turmoil in inter-particle forces. This period lasted until the sand particles attained a more stable packing state. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test ID** & \(\epsilon_{\rm c}\) & \(p^{\prime}{}_{\rm c}\)**\({}^{\rm c}\)**kPa** & \(q^{\prime}{}_{\rm f}\)**\({}^{\rm c}\)**kPa** & \(q^{\prime}{}_{\rm peak}\)**: kPa** & \(q^{\prime}{}_{\rm PT}\)**: kPa** & \(q^{\prime}{}_{\rm USS}\)**: kPa** & \(\epsilon_{\rm f}\) \\ \hline S(0):100 & 0.808 & 100 & 177.0 & 44 & 35.8 & 164.7 & 0.291 \\ S(1):100 & 0.805 & 100 & 208.6 & 89 & 55.2 & 203.6 & 0.288 \\ S(5):100 & 0.798 & 100 & 256.7 & 135 & 70.3 & 208.6 & 0.255 \\ S(10):100 & 0.795 & 100 & 312.1 & 175 & 84.2 & 254.3 & 0.231 \\ S(15):100 & 0.791 & 100 & 345.7 & 218 & 91.3 & 263.9 & 0.220 \\Referring to Figure 7b, the perturbations in the \(q^{\prime}-\varepsilon\) trace for specimen S(1):200 ceased at axial strain levels above 2.5% (i.e., >0.025 on the graph). Further, the \(q^{\prime}-\varepsilon\) trace dips at approx. 2.5% axial  
Figure 6: Stress path following undrained shear behavior: (**a**) base sand; (**b**) 1% NS; (**c**) 5% NS; (**d**) 10% NS; (**e**) 15% NS; (**f**) perturbations for 1% NS. strain, and the stress path changes direction (see Figure 6b), marking a state, at which the specimen achieves a local minimum shear strength ahead of strain-hardening. This transition is effectively an event that marks the most pronounced loss of sand particle-to-particle contacts. The subsequent strain-hardening period leads to an increase in the mean numbers of particle-to-particle contacts with increasing strain. Here, the 2.5% axial strain represents a transition point from an initial metastable to a more stable packing state. It will be shown later that the role of NS at this 'threshold' 200 kPa mean effective stress is optimum, resulting in maximum peak deviatoric stress. The observations on plastic volumetric behavior of the base and NS-treated sands are better described in quantified forms, which necessitates the definition of a state index. Flow potential (\(u_{\text{f}}\)) is adopted here as an appropriate state index. [PERSON] and [PERSON] (2016) first suggested the use of \(u_{\text{f}}\), the maximum excess pore-water-pressure ratio, as a measure of softening. The \(u_{\text{f}}\) index is controlled by stress conditions in the sand during both initial and shearing stages. Equation (3) formulates the flow potential as a function of \(p^{\prime}_{\text{PT}}\) (mean effective stress at the PT point) and \(p^{\prime}_{\text{c}}\) (mean isotropic effective confining pressure):  
\[u_{\text{f}}=1-\frac{p^{\prime}_{\text{PT}}}{p^{\prime}_{\text{c}}} \tag{3}\]  
The variation of the flow potential with NS content is presented in Figure 8 for the base and modified sands. Relatively higher flow potential values were measured for base sand specimens under the lowest confining pressures investigated. Generally, the flow potential appears to be approx. indirectly proportional to NS content and the \(p^{\prime}_{\text{c}}\) level. Figure 7: Stress-strain traces for undrained triaxial compression of base and NS-treated sands isotropically consolidated for \(p^{\prime}_{\text{c}}\) values of: (**a**) 100 kPa; (**b**) 200 kPa; (**c**) 300 kPa; (**d**) 400 kPa. The above findings are consistent with similar attempts (but with different chemical grout proppants employed) in the investigations by [PERSON] [39], [PERSON] and [PERSON] [40] and [PERSON] and [PERSON] [41], and also where cement was used as additive in the studies by [PERSON] et al. [42] and [PERSON] et al. [43]. As described earlier, NS treatment had minimal impact on the post-consolidation void ratio and packing state of the sand specimens but reduces strain-softening behavior.