## 3 Undrained Shear Behavior for Binary Mixtures  
A series of undrained triaxial compression tests was performed on the base and treated sand specimens, investigating 1%, 5%, 10% and 15% NS contents. The specimens were sheared monotonically by axial compression to >40% axial strain in order to reach or closely approach the critical state. Table 5 presents a summary of the testing program and steady states. Figure 6 shows the shear responses in the \(q^{\prime}-p^{\prime}\) plane of the base sand and four NS-treated sand mixtures. Stress paths are plotted for four initial mean effective stresses (\(p^{\prime}{}_{\rm c}\) = 100-400 kPa), with the post-consolidation void ratio (\(e_{\rm c}\)) adopted as the basis for comparison. Figure 5: State transitions during undrained shearing of isotopically-consolidated triaxial specimens: (**a**) phase transformation state; (**b**) steady states ([35] with modifications). Two immediate observations are discussed here: (1) the variation in \(\epsilon_{\rm c}\) with \(p^{\prime}{}_{\rm c}\) was marginal for all test specimens, as one would expect for saturated granular soils; (2) for both base sand and binary mixtures, greater confining pressures diminished the strain-softening. These points collectively illustrate the significant control of confinement pressure on the post-yield behavior of saturated granular materials. The addition of colloidal NS to the F161 sand generally decreased the strain-softening response, as compared with the base sand at a nearly similar void ratio. To test this observation, the mean effective stress at phase transformation (\(p^{\prime}{}_{\rm PT}\)) is adopted here as a proxy parameter. That is, the phase transformation marks the transition from a structurally metastable state to a more stable state, when a local minimum shear strength is reached, and further straining increases the average number of sand particle-to-particle contacts. To demonstrate, the phase transformation (\(p^{\prime}{}_{\rm PT}\)) for the base sand and binary mixtures comprising 10% and 15% NS contents are compared. An initial effective stress (\(p^{\prime}{}_{\rm c}\)) of 200 kPa is adopted as it was found to produce the minimum variations of void ratio with NS content (Figure 4). The post-consolidation void ratio values for specimens S(0):200, S(10):200 and S(15):200 were 0.783, 0.775, and 0.773, respectively. This marks a gentle but negligible decrease in void ratio upon groatt treatment. With reference to Figure 6a, phase transformation was reached at a low \(p^{\prime}{}_{\rm PT}\) of 142 kPa for base sand, indicating a strong strain softening. For S(10):200 and S(15):200, \(p^{\prime}{}_{\rm PT}\) increased to 151, and 180 kPa, respectively (see Figure 6d,e), marking a much lower \(p^{\prime}{}_{\rm PT}-p^{\prime}{}_{\rm c}\), and hence relaxed strain-softening. Our findings indicate that grouting sand with NS leads to a gradual transformation of the base sand into a geocomposite possessing stiffer, more brittle, and more dilative stress-strain behavior. This transition appears to be controlled by the mean effective stress--that is, in Figure 6a-c, the strong strain softening in base sand for low \(p^{\prime}{}_{\rm c}\) (\(\leq\)200 kPa) continues to appear for the 1-15% NS-treated sand specimens, but vanishes at greater \(p^{\prime}{}_{\rm c}\) levels. Referring to the characteristic stress path in Figure 5a, the transition footprint can be seen in the experimental \(q^{\prime}-p^{\prime}\) traces presented in Figure 6b-c and in the \(q^{\prime}-\epsilon\) traces through the initial stage of shearing, with \(p^{\prime}{}_{\rm c}=200\) kPa, where binary mixtures with \(<\)5% NS content exhibited some clearly visible minor fluctuations in the stress paths (Figure 6a-b). These perturbations (Figure 6f) were less pronounced at the higher \(p^{\prime}{}_{\rm c}\) levels investigated.