# Resilient Modulus Characterization of Compacted Cohesive Subgrade Soil
## 3 Results and Discussion
### Analysis of Resilient Modulus Value  
The hysteresis loops were analyzed and the value of \(M_{r}\) was established for nineteen tests. The additional values of \(M_{r}\)_max_, which characterizes the modulus with maximal slop on the stress-strain plot, were also calculated (see Figure 7). The purpose of these calculations was to evaluate the correlation between maximal resilient modulus and \(E_{max}\). The resilient modulus had different values for each of the applied deviator stress levels, and the \(M_{r}\)_max_ values were also different for each test. The recoverable strains characterized by the resilient modulus \(M_{r}\) are presented in Figure 8a-c for tests in \(\sigma^{{}^{\prime}}_{3}\) equal to 45 kPa, 90 kPa, and 135 kPa, respectively. The \(M_{r}\) value in the first cycle was between 44 and 59 MPa for confining pressure \(\sigma^{{}^{\prime}}_{3}\) equal to 45 kPa and between 48 and 78 MPa for \(\sigma^{{}^{\prime}}_{3}\) equal to 90 kPa. For \(\sigma^{{}^{\prime}}_{3}\) equal to 135 kPa the \(M_{r}\) value was between 45.0 to 81.1 MPa. During cyclic loading, the resilient modulus value decreases to around \(10^{3}\) cycles. Then, in the case of plastic creep strain response, the \(M_{r}\) value increases in the rest of the tests. The resilient modulus \(M_{r}\) decrease was caused by strain development between \(10^{2}\) and \(10^{3}\) cycles. This can be observed as the \(M_{r}\) value decreases on plots 8a-c and indirectly on plot 3a-c. After this stage, the \(M_{r}\) value increases. The reason for that is the increase of stiffness which can be observed as smaller resilient strains in one cycle. During this phase, the stress path has not changed its value (see Figure 5c,d), the equilibrium state is achieved, and no further changes of the resilient modulus value occurs. Figure 6: Young modulus \(E_{max}\) versus shear strain amplitude for isotropically-consolidated sandy clay (\(\sigma^{{}^{\prime}}_{3}\) = 45 kPa and \(\sigma^{{}^{\prime}}_{3}\) = 90 kPa); RCA—resonant column test; TS—torsional shear test for a frequency of 1 Hz. Figure 8: Resilient modulus value of tested sandy clay for different conditions: radial stress \(\sigma^{\prime}_{3}\) equal to (**a**) 45 kPa; (**b**) 90 kPa; and (**c**) 135 kPa, as defined in Table 2.  
Figure 7: Schema of the hysteresis loop for \(M_{r}\) and \(M_{r\max}\) calculations. The differences in the \(M_{r}\) value are clearly dependent from the deviator stress levels, which causes decreased soil strength in further steps during this test. The deviator stress also causes different responses of the soil. In the case of the tests conducted in radial stress \(\sigma^{\prime}\)3 equal to 45 kPa, the \(M_{r}\) average values was between 41.8 to 70.5 MPa. Four stages of cyclic loading were characterized by lower values of \(M_{r}\) and were between 41.8 to 49.9 MPa. The Stages 1.5 to 1.8 showed another \(M_{r}\) value development. The resilient modulus rises from 47.6 MPa to 70.5 MPa. The \(M_{r}\) value for tests conducted at radial stress \(\sigma^{\prime}\)3 equal to 90 kPa ranged between 43.0 and 65.3 MPa. The average value of resilient modulus in first stage of repeating loading varies form 44.7 MPa to 56.3 MPa. The test results for \(\sigma^{\prime}\)3 equal to 90 kPa indicate that the \(M_{r}\) value decreases with rising deviator stress \(q_{max}\), which is not so clear in the case of tests where \(\sigma^{\prime}\)3 is equal to 45 kPa. After the specimen rises to a critical state, the \(M_{r}\) value rises from 43.0 to 55.8 MPa. The tests performed in \(\sigma^{\prime}\)3 equal to 135 kPa show other characteristics. The average resilient modulus in the first stages is low and rises in Stages 3.2 and 3.3, where it reaches a maximum value. In Stages 3.4 to 3.9 decreases occur due to pore pressure.