# Stability of a Compacted Sand Slope Model Subject to
## 4 Conclusions  
This study determined the failure load of a slope model made up of a compacted sand. The applicability of such an investigation is wide and should be followed up, during the construction phase, in terms of the stability of excavations in the presence of surcharge loads. An experimental investigation in the laboratory involved the preparation of a slope model, and then loading tests were conducted using an imposed rate of vertical displacement at the crest side. Two angles of the slope models, \(\alpha\) = 30\({}^{\circ}\) and 35\({}^{\circ}\), and various locations of the applied loading were analyzed for ten slope models. Then, the slope test models were simulated by performing a 3D numerical study using Plaxis code and adopting the Mohr-Coulomb and hardening soil constitutive laws for the compacted sand. The main outcomes of the experimental, numerical and analytical investigations are sum \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test Models**} & \multicolumn{3}{c}{**Failure Loads (kN)**} \\ \cline{2-4}  & **Analytical** & **Experimental** & **Numerical** \\ \hline M3 & 1.04 & 0.50 & 0.51 \\ \hline M4 & 0.77 & 0.85 & 0.83 \\ \hline M5 & 1.04 & 0.86 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison between the recorded failure load of test models M3, M4 and M5 and the numerical and analytical predictions. marized hereafter. Experimental and numerical results confirmed that the failure load decreases when the angle of the slope model increases from 30\({}^{\circ}\) to 35\({}^{\circ}\). For a given slope angle, the closer the applied loading to the slope side, the smaller the failure load. Predicted values of the failure load by the Mohr-Coulomb constitutive law fit better with measurements for the majority of tested slope models with a relative difference of less than 11%. On the other hand, only one prediction by the HSM proved to be satisfactory (relative difference equals 3.5%) for a slope test model with an angle of 35\({}^{\circ}\). However, the globally observed behavior (load-displacement curves) of the tested slope models proved to be better described either by the Mohr-Coulomb constitutive law or by the hardening soil model depending on the value of the angle of slope model and the location of applied loading. Considering the framework of the YDT and from the experimental results, the log-spiral curve was determined to be the best model in reproducing the observed failure mechanism. Assuming the Mohr-Coulomb strength criterion, the analytical plane strain condition can predict a reasonable upper-bound value of the failure load of the sand slope model. The present paper did not address water drainage within the compacted sand slope, i.e., the absence of a water table. This limitation will be addressed in future work. Conceptualization, S.D. ; Software, H.K. ; Validation, W.F. ; Investigation, S.D. and M.B. ; Resources, M.D., T.N. and M.E.M. ; Writing--original draft, M.B. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. The elasticoplastic non-linear isotropic strain hardening model, or the well-known HSM, was suggested to reproduce the observed macroscopic phenomena for grounds [19]:  
* Densification, decrease in the volume owed to the plastic deformations (distortions);
* Increase in stiffness with depth;
* Stress-strain history taking account of pre-consolidation effect;
* Dilatancy (resp. contractancy) increase (resp. decrease) in volume. Contrarily to other models such as the Modified Cam Clay, the amplitude of deformations (distortions) of the soil needed the incorporation of three stiffness parameters: the rigidity of triaxial loading (E\({}_{50}\)), the rigidity of triaxial unloading-reloading (E\({}_{\text{ur}}\)), and the edometer modulus (E\({}_{\text{ped}}\)). Figure 14 displays the stiffness moduli considered by the HSM in the deviator-axial strain plan as usually recorded during shear triaxial test.