## 3 Results and Discussion
### Assessment of State Properties and Susceptibility to Liquefaction  
Liquefaction flow is responsible for catastrophic damage triggered by sudden ruptures, spreading the liquefied material over large areas. In this context, based on the previously proposed classification system, an analysis was carried out to evaluate the flow potential due to the liquefaction of soil based on concepts from the critical state theory. According to [PERSON] [34] and [PERSON] et al. [38], the value of state parameter \(\psi\) in sands can be obtained from a theoretical equation dependent on the \(G_{o}/q_{t}\) ratio. It is intended to investigate the applicability of this equation also for use in mining tailings (non-plastic silts). Considering the results of cone tests and tests with seismic readings, [PERSON] and [PERSON] [34] presented a theoretical correlation calibrated through tests conducted in a calibration chamber for determining the state parameter of clean sands, as presented by Equation (8). \[\psi=\alpha\left(\frac{p^{\prime}}{p_{a}}\right)^{\beta}+\chi\ \ln\left(\frac{G_{o}}{q_{c}}\right) \tag{8}\]  
where \(\alpha=-0.520\), \(\beta=-0.07\), and \(\chi=0.180\) are average coefficients obtained from the data of tests in the calibration chamber, and \(p^{\prime}\) is the average effective stress acting on the material. Whenever the material is in a dense state, with a void content initial value lower than the void ratio in the critical state, the material will have a dilatant behavior during shear, and \(\psi\) will assume a negative value. On the other hand, when the soil is in a soft state, with an initial void ratio higher than the critical void ratio, the soil will compress during shear, and \(\psi\) will assume a positive value. The conditions necessary for liquefaction flow in materials from the leftmost regions of the classification graph are different from those for materials located further to the right of the graph. In this way, knowing that both the soil classification system and the determination of the state parameter depend on the values of stiffness (\(G_{o}\)) and resistance (\(q_{t}\)), an equation was developed for delimiting  
Figure 9: Estimation of internal friction angle (\(\phi^{\prime}\)), undrained strength (\(S_{u}\)), unit weight (\(\gamma\)), and \(I_{c}\) index. curves, with values defined from \(G_{\rm o}\), for which the state parameter is equal to zero. These curves were plotted with the classification system, as shown in Figure 10. The development of the soil classification system is based on theoretical formulations grounded in cavity expansion theory and critical state theory. This system allows for behavior analysis by combining stiffness and resistance parameters. In the case of application to sandy soils of the experimental field studied herein, the significant advantage of the system is linked to the identification of partial drainage conditions and the determination of a region for non-plastic sensitive materials, in which the generation of excess pore pressures occurs during cone penetration, with a significant reduction in tip resistance. Thus, Figure 10 presents the relationship between \(G_{\rm o}/q_{\rm t}\) for the CPTu results, whose outcomes were compared to values in the calibration chamber for a stress range between 50 and 5000 kPa. It is observed that for a certain stress level, the ratio of \(G_{\rm o}/q_{\rm t}\) decreases with the reduction of the state parameter value \(\psi\); that is, \(G_{\rm o}/q_{\rm t}\) decreases with the increase in the relative density of the material. As presented in Figure 10, the data recorded on the CPTu tests demonstrates that soils are classified as dilative material. In this context, the material is susceptible to liquefaction, as explained by [PERSON] et al. (2013, 2014). Keeping the \(G_{\rm o}\) value fixed, the state parameter decreases to the right of the presented curve and increases to the left.