## Interpretation of Results
### Cyclic and Permanent Strain
#### 5.4.2 Qualitative Evaluation  
The qualitative analysis of the results is carried out based on the information included in Figure 9, focusing on the stress-strain behavior, cyclic strains and number of cycles, permanent strains and number of cycles, and the influence of the monotonic shear stress (\(\tau_{\rm o}\)) applied previously to the cyclic shear stress (\(\tau_{\rm c}\)) in the generation of cyclic (\(\gamma_{\rm c}\)) and permanent strains (\(\gamma_{\rm p}\)). Table 1 is represented within this Figure 9, indicating with a letter from A to L the different types of stress-strain curve obtained in the tests for each combination of static and cyclic shear stress. Each of the different curves is presented on the outside of the Table. Figure 8: Stress-strain definitions. Figure 9: Comparison of typical stress-strain behavior for different combinations of normalized initial monotonic shear stress and different normalized cyclic shear stress. The results correspond to the tests performed with sample SIA-10 indicated in Table 1. (A) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 0% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 25%; (B) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 5% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 25%; (C) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 10% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 20%; (D) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 15% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 20% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 25% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 5%; (G) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 20% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 5%; (G) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 20% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 5%; (H) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 15% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 10% (J) \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 50% and \(\tau_{\rm c}/\sigma^{\prime}\)\(w\) = 20%. The analysis was performed by comparing the behavior of the samples that meet the following conditions:  
* Same normalized initial monotonic shear stress (\(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\)) and different normalized cyclic stress (\(\tau_{\text{c}}\)/\(\tau^{\prime}_{\text{ov}}\)). * Same normalized cyclic stress (\(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\)) and different initial normalized monotonic shear stress (\(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\)). * Same sum of the normalized initial monotonic shear stress (\(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\)) plus the normalized cyclic shear stress (\(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\)). In particular, for cases where the sum is equal to 25% and 30%. The sum equal to 30% corresponds approximately to the monotonic tests in which \(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}=\tau_{\text{max}}\)/\(\sigma^{\prime}_{\text{ov}}\)\(\approx\) 30%. From the information included in Figure 9, related to the stress-strain behavior, the following considerations were deduced:  
* For a constant value of \(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\) and of the number of cycles and a different \(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\), the cyclic (\(\gamma_{\text{c}}\)) and permanent (\(\gamma_{\text{P}}\)) strains increase as \(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\) is higher. * For a constant value of \(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\) and \(\gamma_{\text{c}}\), and with a different \(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\), the number of cycles decreases as \(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\) increases. * For a constant value of \(\tau_{\text{c}}\)/\(\sigma^{\prime}_{\text{ov}}\) and a different \(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\), the loops of the cycles gradually change their geometry formed by \"s\" and \"s inverted\", for values of \(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\) lower than 10%, to a geometry formed by a concave and a convex curve, for values of \(\tau_{\text{o}}\)/\(\sigma^{\prime}_{\text{ov}}\) greater than 10%.