## 5 Conclusions  
In this paper, a numerical model of spudcan penetration into sand overlying clay with the CEL approach is proposed. An M-C model incorporating both stress-dependence and strain-softening is proposed for sand. Furthermore, the strain softening effect is also considered for clay. Sensitivity analysis and verification of the model are performed. All the studies show the following:  
* The peak and post-peak resistances in the sand layer increase with the critical threshold of accumulated deviatoric shear strain. However, the peak resistance will converge at a certain value of \(k^{c}_{shear}\) (0.5 for the case of Figure 6). No significant peak resistance is observed for \(k^{c}_{shear}=\infty\) (non-strain softening of sand). The resistance in the underlain clay is barely affected by \(k^{c}_{shear}\). The resistance at the sand-clay interface decreases about 10% from \(S_{t}=1\) to 3, while the resistance profiles are nearly identical for \(S_{t}=3\) and 5.
* The proposed model agrees very well with the centrifuge test of spudcan penetration into uniform sand. The penetration in shallow depth is well simulated due to the incorporation of the stress-dependence behavior of sand. Furthermore, the relatively slow increasing rate of resistance is captured by the strain-softening model of sand.
* The spudcan penetration resistance in loose sand overlying clay is also well simulated. However, the resistance in shallow depth is a little overestimated, which is very probably attributed to the assumption of constant peak friction angle for \(k_{shear}<k^{p}_{shear}\), providing the fact that the peak friction angle of sand needs a process to be mobilized.
* The numerical model captures the peak resistance and post-peak profile in dense sand overlying clay relatively well. However, it underestimates the peak resistance and overestimates the resistance in the underlain clay layer. The difference may be due to the selection of \(\Delta\phi=3^{\circ}\) obtained from triaxial tests, which is different from the real process of spudcan penetration conditions.  
The proposed method provides a framework for the numerical analysis of geotechnical engineering in sand. The prediction accuracy of the model depends on the parameters. Those parameters involved should be determined based on geotechnical tests. Otherwise, inappropriate selection of the parameters may induce errors.  
Figure 11: Penetration resistance profiles from centrifuge tests and numerical analysis (dense sand overlying clay) [11].  
**Author Contributions:** Conceptualization, P.G. and M.L.; Data curation, S.Y.; Formal analysis, S.Y.; Funding acquisition, P.G., J.C., and M.L.; Investigation, P.G. and J.C.; Methodology, P.G.; Supervision, M.L.; Validation, S.Y.; Writing--original draft, P.G.; Writing--review and editing, J.C. and M.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research and the APC were funded by the Natural Science Foundation of China, grant number 51709164, 51909030. This study was also supported by the Open Project Program of Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development (Grant No. BIPT2020004).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Acknowledgments:** Many thanks are given to [PERSON] for her kind help in improving the English writing of this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.