## 3 Numerical Results
### Case of a Rigid Slab Over a Mattress of 100 mm on Reinforced Soil (D100)  
#### 3.1.1 Soil Arching  
Figure 8 compares the numerical results and the experimental data of pile efficacy as a function of the pressure on the slab top (\(p\)) under the monotonic test M_D100. In overall, the efficacy increases as the vertical surcharge increases. The numerical curve of HYP model shows that the pile efficacy dramatically increases from 30% to about 90% as the vertical pressure rises from 0 to 10 kPa. Meanwhile numerical curve of CYsoil model experiences a lower pile efficacy of 20% at the pressure of 10 kPa. Both numerical results \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Type/Parameters** & \(\kappa\) & \(\
u\) & \(\lambda\) & \(M\) & \(a_{0}\)(kPa) & \(e_{o}\) \\ \hline Compressible soil & 0.02 & 0.3 & 0.9 & 1.30 & 3000 & 7.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The MCC model parameters considered for the compressible soil. Figure 7: Experimental and numerical results in the oedometer test for the compressible soil sample. then show a slight increase in pile efficacy in following loading process. Regarding the experimental curve, after activating the weight of the LTP, the efficacy value is about 30%. It then increases significantly of 60% to reach a peak at a pressure of 8 kPa followed by a plateau till the pressure of 18 kPa. After that, it gradually reduces from 90 to 70% as the loading increases from 18 to 30 kPa. Figure 9 depicts the variation of the soil arching, in terms of pile efficacy, with respect to the load cycles number (C1_D100 test). In general, the pile efficacy decreases as the number of cyclic loading increases. This tendency was also presented in the study of [PERSON] et al. (2008) [2], in which the arching ratio reduced from 76 to 56% for 700 load cycles. This can be explained by the grain rearrangement which occurs during the cyclic loading. While the numerical results for the HYP and CYsoil models showed a decrease in the pile efficacy with the load cycles number, the experimental data shows that the pile efficacy increases slightly during the first 30 load cycles. It is subsequently followed by a slight decrease. The pile efficacy of the HYP model is in good agreement with the experiment data at the beginning, reaching a value of nearly 82%. It then decreases slightly with the number of load cycles. Meanwhile, the pile efficacy of CYsoil model is about 15% lower. Figure 10 presents the experimental and numerical results of the pile efficacy in the test C2_D100. Similarly to the C1_D100 test, there is an increase in the experimental efficacy in the first 30 cycles. However, the increase is insignificant. The pile efficacy using the HYP model is closer to the experimental data than that the CYsoil model one. The two loading cases are compared in Table 5. The pile efficiency in both tests is similar. It means that the cyclic loading range considered does not significantly affect the soil arching development. Figure 8: Experimental and numerical efficacy coefficients in test M_D100. Figure 9: Experimental and numerical efficacies in test C1_D100. The evolutions of the vertical stresses applied to the inclusion head and soft soil under the number of loading cycles in test C1_D100 is presented in Figure 11. Using the HYP model for the LTP in the numerical analysis, an insignificant decrease in the inclusion head stress and a slight increase in the soft soil stress are observed. As presented by [PERSON] (1996); [PERSON] et al. (2010) [32; 33], a cohesionless soil subjected to cyclic loads induces cumulated strains that cause its stiffness degradation. Therefore, the expansion of plastic zones and the decrease in the inclusion head stress under cyclic loading can be explained by the stiffness degradation. Soil experimental data under cyclic loading is then necessary to accurately calibrate the parameters for the stiffness degradation curve simulation.