## 5 Conclusions  
In this study, a new method was proposed for slope reinforcement by a spatial arc crown beam composite supporting structure. First, a laboratory model test was carried out to investigate the distribution regularity of the bending moment along the pile. Subsequently, a numerical model was developed using the finite element method for simulating the slope, and it was then verified by the measured data from physical model tests. Finally, a full-scale slope numerical model was developed to further analyze the distribution regularity of the pile displacement, soil pressure, as well as the influence from the crown beam stiffness upon the bending moment and the axial force of crown beam. Based on the lab-scale model test and the numerical results, the following conclusions were reached:  
1. The spatial arc crown beam is simplified to a two-hinged arch. Compared with the straight crown beam, the maximum value of the bending moment in the arc crown beam is about one-third the quantity of the straight crown beam through theoretical calculation.
2. The spatial arc crown beam redistributes the load among different piles. The extreme values of the piles not at the slope foot vary within 10% along the downhill direction, and thus the mechanical characteristics of pile are more reasonable.
3. The bending moments are close to zero at the pile end, and the pile tops are connected through the arc crown beam. Thus, the anti-slide pile can be simplified as a vertical beam with one end fixed and one end hinged.
4. The axial force in the spatial arc crown beam is always presented as pressure. Therefore, the crown beam can make full use of the compression resistance of concrete and avoid the bending-shear failure in a straight crown beam.
5. The distribution characteristic of soil pressure in front of pile near the arch foot is different from that in other positions. The stable soil at the slope foot provides greater soil resistance for anti-piles than that in other positions. Although the soil pressure in front of the pile top is zero at the slope foot, the anti-slide piles are still within normal work conditions and thus can avoid the soil destruction in a large area.
6. As crown stiffness is above five times the reference value, the axial force of the crown beam tends to be stable. However, the stiffness increases continually to 20 times that the reference value. The maximum value of \(M_{y}\) is \(-\)1013.13 kN\(\cdot\)m, and the constraining effect of the crown beam is gradually weakened.  
Conceptualization, Y.D.; Methodology, Y.D.; Software, Z.Y.; Validation, Z.Y.; Investigation, W.L. and K.Z.; Data curation, Z.Y. and C.P.; Writing--original draft, Z.Y.; Writing--review and editing, Y.D.; Project administration, Y.D.; Funding acquisition, Y.D. All authors have read and agreed to the published version of the manuscript.  
The research described in the paper was supported by National Natural Science Foundation of China (Nos. 51878554 and 41672308) and Key Projects of Shaanxi Natural Science Basic Research Program (No. 2018 JZ5012).  
Figure 22: \(M_{y}\) of crown beam.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data generated or analysed during this study are included in this published article.  
**Conflicts of Interest:** The authors declare no conflict of interest.