## 6 Discussion and Concluding Remarks  
Being inspired by the removal process of a nail from wood or a steel block, we applied the force analysis to a helix in sand; a theoretical model was proposed in this paper to predict the recycling torque of the single-plate helical pile in sand. In order to verify the accuracy and practicability of the theoretical model, a series of tests were conducted to analyze the influence of the outer diameter of the helix, \(D_{\text{H-out}}\), the pitch of helix, \(p\), the recycling speed of helical pile, \(v_{\text{R}}\), and the vertical force on the central shaft, \(F_{\text{push}}\), and the recycling torque, \(T_{\text{R}}\). According to the test results and the results of theoretical model, some conclusions were accumulated below:  
1. The theoretical results and the test results both show the size of the helix (the outer diameters of helix, \(D_{\text{H-out}}\), and the pitches of helix, \(p\)) have great influence on the recycling torque of the single-plate helical pile. The recycling torque, \(T_{\text{R}}\), of the single-plate helical pile increases with a rise of the outer diameter of the helix, \(D_{\text{H-out}}\), when the recycling speeds of helical piles, \(v_{\text{R}}\), and the pitch of helix, \(p\), are the same.
2. For the pitch of helix, \(p\), it changes the weight of the soil which is on the top of the helix and changes the recycling torque indirectly when the embedment of helix is constant.
3. The recycling speed of helical pile, \(v_{\text{R}}\), also has effect on the recycling process of single-plate helical pile. The vertical force on central shaft, \(F_{\text{push}}\), and the recycling torque, \(T_{\text{R}}\), of the single-plate helical pile both increase with the rise of the recycling speed of the helical pile, \(v_{\text{R}}\); however, the recycling speed of helical pile, \(v_{\text{R}}\), does not influence the recycling torque directly; it has a direct relationship with the vertical force on central shaft, \(F_{\text{push}}\).
4. For the vertical force on central shaft, \(F_{\text{push}}\), has a direct relationship with the recycling torque, \(T_{\text{R}}\), of single-plate helical pile. With the rise of the vertical force on central shaft, \(F_{\text{push}}\), the corresponding recycling torque, \(T_{\text{R}}\), increases.
5. The theoretical results are in great agreement with the corresponding experimental results in different conditions. Based on the verification of a series of tests, the accuracy of the proposed theoretical model, which was used to predict the recycling torque, \(T_{\text{R}}\), of single-plate helical piles in sand with different sizes of helix and different vertical forces on the central force, \(F_{\text{push}}\), was proven.  
With this theoretical model, the gap in the research about the recycling torque of a single-plate helical pile is filled and designers can have a helpful reference for predicting the recycling torque of the single-plate helical pile in dense sand, and choose suitable equipment for the recycling of single-plate helical piles in dense sand.  
Conceptualization, H.D. and P.Z.; methodology, H.D., P.Z., and L.W.; test, L.W., Y.L., and P.Z.; validation, Y.T. and P.Z.; formal analysis, L.W. and Y.T.; investigation, L.W., P.Z., and Y.L.; data curation, L.W. and X.Q.; writing--original draft preparation, L.W.; writing--review and editing, L.W., P.Z., and Y.T.; supervision, H.D., P.Z., and Y.T.; project administration, H.D. and P.Z.; funding acquisition, H.D. and P.Z. This research was supported by the National Natural Science Foundation of China (number 51779171, number 51679163), the Innovation Method Fund of China (number 2016 IM030100), and the Tianjin Municipal Natural Science Foundation (number 17 JCYBJC2000). The authors declare no conflict of interest.