## 3 Results and Discussion
### The Effect of Consolidation on the Soil Response to Cyclic Loading
The cycle in the case of sample 2.1 and 2.3 had a small area and greater inclination than in the last cycle of loading. Sample 2.2 and 2.5 were characterized by high excess pore water pressure generation, the big area of the hysteresis curve in comparison to previous tests and the same inclination after 10,000 cycles of loading. The same phenomena can be seen in sample 2.4's response to cyclic loading. The lesser pore water pressure value might be caused by a low initial void ratio. In Figure 11, the comparison of laws cycle of loading for excess pore water pressure and the deviator stress increment in one cycle was presented. The tests on the isotropically consolidated samples showed that for the same initial void ratio, the excess pore water pressure generated in one cycle had the same value for equal stress conditions. Sample 1.2, which was more compact, had lower generated excess pore water pressure in comparison to deviator stress conditions that corresponds to the previously observed phenomena. The \(\Delta u/q_{max}\) ratio was equal to 0.195, 0.122, and 0.200 respectively. The \(K_{0}\)-consolidated samples behaved in a similar way. Sample 2.1 with an \(e_{0}\) equal to 0.333 had the \(\Delta u/q_{max}\) ratio equal to 0.108, which corresponds to sample 1.2 where \(e_{0}\) was equal to 0.345. The sample 2.2 with an initial void ratio equal to 0.399 had the \(\Delta u/2q_{a}\) ratio equal to 0.170. This relationship was almost linear for all five samples. Based on this test the conclusion could be formed, the excess pore water pressure in one cycle in long-term cyclic loading test depended on the deviator stress amplitude and the initial void ratio. This indicates that the consolidation type would not impact on this characteristic. Nevertheless, the differences could be seen in the inclination of the stress-strain and excess pore water pressure-strain characteristics. Figure 11: Excess pore pressure and deviator stress versus axial strain for the last cycle of loading from the triaxial tests: (**a**) Isotropically consolidated samples, and (**b**) \(K_{0}\)-consolidated samples. For \(K_{0}\)-consolidated samples' \(\Delta u/q_{max}\) ratio had a linear relationship with \(q_{m}/q_{a}\), which indicates that the excess pore water pressure value in one cycle impacted the deviator stress characteristics. The inclination of the hysteresis loop can be described by the modulus conception. The stress-strain characteristics in cyclic loading are often explained with the resilient modulus definition. The resilient modulus \(M_{r}\) is a quotient of cyclic stress and resilient strain and for the purpose of this study can be defined as:  
\[M_{r}=\frac{q_{max}-q_{min}}{\varepsilon_{max}-\varepsilon_{min}}=\frac{\Delta q }{\varepsilon_{r}}=\frac{2\cdot q_{a}}{\varepsilon_{r}}. \tag{1}\]  
The deviator stress difference is the cyclic stress in one cycle. Therefore, the cyclic stress can be defined as a double deviator stress amplitude in one cycle. The resilient strain is accordingly the maximum and minimum strain observed in one cycle. Another type of soil modulus that can help to understand how excess pore water pressure impacts on the soil stiffness in one cycle is the excess pore water pressure modulus \(M_{\Delta u}\), which can be defined as the quotient of excess pore water pressure in one cycle to resilient strain:  
\[M_{\Delta u}=\frac{u_{max}-u_{min}}{\varepsilon_{max}-\varepsilon_{min}}=\frac {\Delta u}{\varepsilon_{r}}. \tag{2}\]  
The presented relationship between strain and stress components can be used for the evaluation of the hysteresis curve inclination change. On Figure 12 the resilient modulus and excess pore water pressure modulus for isotropically consolidated samples are presented. For the sample consolidated in \(\sigma^{\prime}{}_{3}\) equal to 45 kPa, the resilient modulus characteristic was very similar to the excess pore water pressure modulus. The \(M_{r}\) value first rose and then around cycle 50 reached its maximum value.