# Mechanical Behavior of a Mine Tailing Stabilized with a Sustainable Binder
## 3 Experimental Program
### Results Analysis  
#### 3.2.1 Isotropic Consolidation Test  
The isotropic consolidation curve (ICC) obtained is shown in Figure 8. The results show that the tailing is much less deformable in the unloading and reloading cycles than in the first loading cycle.  
Figure 7: Microstructure of the fly ash obtained by SEM.  
The critical states theory by [PERSON] (2016) [26] was applied to determine the isotropic consolidation line and the critical states line (CSL). The volumetric compression of the tailings was evaluated until failure using the variation of the void index, expressed in terms of the specific volume (\(v\)). This parameter was calculated based on Equation (1).  
\[v=1+e \tag{1}\]  
Figure 9 shows the delimitation of the isotropic compression and expansion lines.  
The line OACD, corresponding to the first loading, is called the normal compression line (NCL) and is given by:  
\[v=N-\lambda\ln\left(p^{\prime}\right) \tag{2}\]  
where \(\lambda\) is the gradient and N is the value of \(v\) for p\({}^{\prime}\) = 1 kPa. The NCL of the mine tailing resulted in a value of \(\lambda\) = 0.101 and N = 2.2795. The BAC line is called the unloading-reloading line (also called the k-line) and is given by:  
\[v=v_{k}-k\ln\left(p^{\prime}\right) \tag{3}\]  
Similarly to the NCL parameters, k is the gradient, and \(v_{k}\) is the value of \(v\) for p\({}^{\prime}\) = 1 kPa. The k-line of the mine tailing resulted in a k = 0.01 and \(v_{k}\) = 1.6856.  
Once the NCL was defined, the critical states line (CSL) was determined. The CSL was defined based on the failure points of the specimens submitted to triaxial compression  
Figure 8: Isotropic consolidation curve of the mine tailing.  
Figure 9: Isotropic compression and expansion curve.  
tests for confining the stresses of 50 kPa, 100 kPa and 200 (NC) kPa. The trajectory of the effective stresses in relation to the trajectory of the total stresses was represented in blue, according to the system (\(\upsilon\), ln (p')). As the test was carried out in undrained conditions, the variation in the specific volume is null, and therefore, the trajectories result in horizontal straight lines. The resulting CSL is represented in Figure 10. As the specimens presented stress trajectories with different lengths, the CSL was defined based on an average of the trajectories of the three tested specimens (Figure 11). The stress trajectory for the specimen with \(\sigma_{3}=200\) (OC) kPa is also represented in green. The failure trajectory of this specimen ended in the CSL. The CSL was defined based on Equation (4).  
\[\upsilon_{\rm c}=\Gamma-\lambda\ln\left(\rm p_{\rm c}\right) \tag{4}\]  
where index \(\rm c\) indicates ultimate failure, \(\lambda\) represents the gradient of the isotropic CSL and NCL, and \(\Gamma\) the value of \(\upsilon_{\rm c}\) for p' = 1 kPa. The CSL of the mine tailings resulted in a value of \(\lambda=0.102\) and \(\Gamma=2.2771\).  
Comparing the expressions determined for the NCL and the CSL, it is verified that the two lines are practically parallel since they present very similar gradient (\(\lambda\)) values. Furthermore, the value of N obtained is slightly higher than the value of \(\Gamma\). The parameters  
Figure 11: Detail of the stress trajectory and definition of the CSL.  
Figure 10: Isotropic consolidation curve with respective NCL and CSL.  
\(\lambda\), \(\Gamma\) and k are constants and translate some intrinsic properties of the material under study. [PERSON] (2016) [26] defined values for these critical state parameters for some typical soils (Table 3). Considering the values presented by the author, the critical state parameters defined that the mine tailing reasonably resembles the typical behavior of Santa Clara clay.