## 3 Numerical Results
### Case of a Rigid Slab Over a Mattress of 100 mm on Reinforced Soil (D100)
#### 3.1.2 Settlements  
The settlements at the LTP base are presented under monotonic and cyclic loading tests. An increase in the surcharge results in a settlements increase, as presented in Figure 12. There is a rather good quantitative agreement between numerical results and experimental. The settlements are approximately equal to 33 mm, corresponding to a surcharge loading of 30 kPa. Irrecoverable settlements are observed in the unloading phase. Additionally, as can be seen from Figure 12, the result given by the HYP are in better accordance that the ones obtained with the CYsoil model.  
Regarding the cumulative settlements at the LTP base induced by the cyclic loading test C1_D100, Figure 13 describes the experimental and numerical cumulative settlements.  
As can be seen, the cumulation of settlements with the number of loading cycles is figured out, but the cumulation per cycle reduces gradually with the cycles. It leads to a rate decrease in the cumulative settlements. The cumulative settlement equals to 6 mm after 10 cycles followed by an increase of 4 mm after the following 40 cycles. There is a good accordance between the HYP model and the experimental data in terms of cumulative settlements. The numerical results of the HYP model for the LTP are more accurate than the CYsoil ones in terms of cumulative settlements. Considering the non-linearity response in the unloading-reloading process allows the constitutive model to better evaluate the cumulative settlements. Figure 14 shows the influence of the load cycles number on the cumulative settlements for the test C2_D100. A similar tendency was obtained with the C1_D100 test, the cumulative settlements with the number of cyclic loads and a good agreement between the numerical results of HYP model and experimental data are observed. As shown in Figure 3, the loading sequence started by an increase of  
Figure 12: Experimental and numerical settlements of LTP base in test M_D100.  
Figure 13: Experimental and numerical cumulative settlements in test C1_D100.  
30 kPa; it then continued by an unloading of 10 kPa, i.e., the test C2_D100 considered the influence of the over-consolidated state of the compressible soil before applying the cyclic loading. A comparison of the two cyclic loading types is presented in Table 6. As it can be seen, the cumulative settlements in the test C2 represent only one third of the C1 test ones. It is because when the loading increases to 30 kPa, the soil pre-consolidation is updated. The following cyclic loading in the C2 test ranges from 10 to 20 kPa and is then within the elastic region. This results in less cumulative settlements induced in test C2 than in C1.  
Table 6 also shows that the cumulative settlements obtained by the CYsoil model are remarkably higher than the one obtained by the experimental test after 50 load cycles. They are doubled in C1_D100 and tripled in C2_D100. The pre-consolidation pressure is not updated in the CYsoil model and its cap enlarged gradually under the loading cycles number. The cumulative settlements given by the HYP one coincide well with the experimental data in both the C1_D100 and C2_D100 tests. The HYP model allows to simulate pre-consolidated soil in terms of load transfer mechanisms and cumulative settlements, after the first load cycle. This is because after a preloading of 30 kPa, the load cycles in test C2 are in the elastic strain range. The intergranular strain concept permits to simulate them accurately.