# Resilient Modulus Characterization of Compacted Cohesive Subgrade Soil
## 3 Results and Discussion  
The triaxial tests were performed in order to, above all, designate the resilient modulus \(M_{r}\) of sandy clay under the changing test conditions. The second objective of the test was to estimate the maximal value of resilient modulus \(M_{r\_max}\) during the first stage of unloading. The permanent strain accumulation was also analyzed. The axial strain \(\varepsilon_{1}\) development during the tests conducted in the triaxial apparatus are presented in Figure 3a-c. The strain observed during this tests indicate three possible ways of soil responding to such loads. The deformation characteristic with the number of cycles \(N\) is distinguished between a stepwise failure, shakedown, and ablation [51]. The concept of deformation which occurs during cyclic loading was later developed to refer to shakedown theory. The three possible categories of material response are:  
* Plastic shakedown, characterized by a rapid decrease of the plastic strain rate, this phenomena is followed by an equilibrium state and fully resilient strains are observed. * Plastic creep is observed when plastic deformation are observed in each cycle or in a cumulative plot of plastic deformation against the number of cycles the increase of deformations are observed. * Incremental collapse, when plastic deformations are great and failure is achieved in a low number of cycles. The tests performed under constant radial stress equal to \(\sigma^{\prime}\)3 45 kPa, in which deviator stress amplitude \(q_{a}\) was equal 5.30 kPa and maximal deviator stress \(q_{max}\) was equal 31.90 kPa, resulted in low strain accumulation and shakedown response. The same permanent deformation characteristic was observed in case of tests 1.2, 1.3, 2.1 to 2.4 and 3.1 to 3.5. The second kind of soil response to cyclic loading, which is plastic creep, was recognized in test numbers 1.4 to 1.6, 2.5 to 2.6, and 3.6 to 3.9. The strain accumulation was higher and a growing tendency of strain accumulation was observed. The incremental collapse phenomena was preceded by the occurrence of shakedown. In other words, plastic creep was not observed in Stage 1.7 and 2.7. The last phenomenon, incremental collapse, occurred in Stages 1.8 and 2.8, but not in the case of tests in \(\sigma^{\prime}\)3 equals to 135 kPa. The strain accumulation displays characteristic growth, which led to failure. All three phenomena were present in the performed tests. The characteristic method of deformation development leads to various resilient modulus values and the resilient response, which can be compared to the elastic phase in the small strain zone. Figure 4a-c show the effective \(p^{\prime}\) stress paths obtained during tests in the radial stress equal to \(\sigma^{\prime}\)3 45 kPa, 90 kPa, and 135 kPa, respectively. The stress path plots show distinctly different mean effective stress paths during cycling and provides a tool to analyze the stress-path evolution. Such evolution happens as a result of pore pressure generation, which increases after numerous cycles, which cause the movement of the stress path toward the critical state line. When the critical state is reached, the stress path moves opposite to the deviator stress axis. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Average Value** & **Standard Deviation** & **Variance** & **Max Value** & **Min Value** \\ \hline Dry soil mass (g) & 1092.0 & 19.8 & 392.3 & 1121.1 & 1067.6 \\ Height (cm) & 13.92 & 0.125 & 0.016 & 14.03 & 13.76 \\ Diameter (cm) & 6.92 & 0.051 & 0.003 & 6.98 & 6.86 \\ Porosity (-) & 0.22 & 0.005 & 0.000 & 0.23 & 0.21 \\ Water mass (g) & 112.28 & 4.707 & 22.155 & 119.60 & 106.70 \\ Full saturation soil mass (g) & 1204.25 & 24.178 & 584.558 & 1240.80 & 1174.30 \\ Soil dry density (g) & 2.09 & 0.003 & 0.000 & 2.09 & 2.08 \\ Moisture (\%) & 0.10 & 0.003 & 0.000 & 0.11 & 0.10 \\ \hline \end{tabular}
\end{table} 
Table 3: The stress parameters of cyclic.