# Dynamic Lateral Response of the Partially-Embedded Single Piles in Layered Soil
## 6 Conclusions  
A dynamic model of the laterally-loaded single pile in layered soil is established employing [PERSON]'s principle based on the modified Vlasov foundation model. The finite difference method and [PERSON]'s function method are combined to obtain the single pile's first-order natural frequencies and dynamic response configuration. Then, numerical results and discussions are presented to explore the single pile's dynamic characteristics  
Figure 8: Effect of the elastic modulus of soil on the dynamic response of the single pile under varied scour levels: (**a**) Free-fixed pile, scour level-0; (**b**) Free-fixed pile, scour level-5 (**c**) Free-free pile, scour level-0; (**d**) Free-free pile, scour level-5.  
and examine the effects of scouring, elastic modulus, and the thickness of layered soil on the dynamic response of the partially-embedded single pile in the layered soil fields. The conclusions are as follows:  
1. As the scour degree intensifies, the subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. Furthermore, the first-order natural frequencies of the single pile in layered soil decrease significantly.
2. When scouring to the length of the non-embedded section of the pile satisfies \(l_{1}\geq L/2\) (\(L\) is the pile length), the partially-embedded single pile will demonstrate lateral instability under the action of dynamic load.
3. As the thickness of the underlying soil increases, the first-order natural frequencies of the single pile under varied scour levels increase. During the response, amplitudes of the pile top decrease.
4. As the elastic modulus of the first layer of soil increases, the first-order natural frequencies of the single pile increase, and the response amplitudes of the pile top decrease significantly, while the displacement amplitudes at the inverted point of the pile body increase. The elastic modulus of the first layer of soil is increased by about 0.5 times, 1 time and 2 times, and the first-order natural frequencies of the single pile increase by about 10%, 20%, and 30%.  
The model in this paper has certain limitations, such as not considering the slip or separation phenomenon of the pile-soil interface and nonlinear dynamic analysis. The pile-soil dynamic response in most sites is particularly complex. As a weak part of the pile foundation, the pile-soil contact surface is prone to the damage of the soil around the pile and even the detachment of the contact surface, which leads to the lack of binding force of the soil and instability of the pile foundation. Therefore, in the future study of the dynamic response of pile foundations, it is necessary to explore the dynamic characteristics of the laterally-loaded piles, considering the weakening effect of the contact surface.  
Conceptualization, J.M.; methodology, J.M. and S.H.; software, S.H.; validation, S.H., X.G. and D.L.; formal analysis, J.M., Y.G. and Q.L.; investigation, X.G. and D.L.; resources, J.M.; data curation, S.H.; writing--original draft preparation, [PERSON] and S.H.; writing--review and editing, [PERSON], [PERSON] and Q.L.; funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (grant number 11502072, 51878265 and 52178331), the Young-backbone Teacher Foundation of Colleges and Universities of Henan Province (grant number 2019 GGJS076) and the Key R&D and Promotion Special Project in Henan Province--Science and Technology Research Project (grant number 212102310946).  
Not applicable.  
The authors greatly appreciate the comments from the reviewers, whose comments helped to improve the quality of the paper.  
The authors declare no conflict of interest.