# Study on Load Transfer Mechanism of Pile-Supported Embankment Based on Response Surface Method
## 4 Conclusions  
Based on the improved three-dimensional finite element model, this paper analyzed and compared the influence of the embankment filler properties and geogrid strength on the load transfer. Firstly, based on the single-factor test, the contribution of the soil arching effect and membrane effect to the load transfer, as well as the variation law of the pile-soil stress ratio under embankment load, were clarified. Then, based on the response surface optimization test, the interactive relationship between the embankment filler properties and the geogrid strength was analyzed, and the original design was optimized. The results showed that:  
1. Using an elastic medium instead of a soft soil subgrade can reduce the calculation depth of the subgrade and improve the calculation efficiency of the model. The calculated values of the model were in good agreement with the measured results of the field test. The theoretical value of the model was calculated according to BS 8006-1 and the Nordic Geotechnical Group, and the change trend of the calculated value, as well as the theoretical value, were basically the same. This proved the rationality of this model. 2. Increasing the cohesion, the internal friction angle, and the elastic modulus of embankment filler can promote the soil arching effect to a certain extent. However, for reinforced embankments, larger cohesion, a larger internal friction angle, and a higher elastic modulus of the embankment will reduce the pile-soil differential settlement, affecting the load transfer and reducing the pile-soil stress ratio. 3. The increase in the geogrid strength had a certain promoting effect on the pile-soil stress ratio. However, when the geogrid strength reached 120 kN/m, the increase in the pile-soil stress ratio was small. 4. The pile-soil stress ratio was more sensitive to the changes of the internal friction angle of the embankment filler and the elastic modulus of the embankment, followed by the cohesion. The sensitivity of the geogrid strength was the lowest. Therefore, it is suggested that in the design of pile-supported embankments, in addition to the main design parameters, such as pile length, pile spacing, and grid strength., the influence of embankment filling properties on the load transfer should be considered. 5. The Box-Behnken design method was used for the experimental design, and the multiple regression model, considering the pile-soil stress ratio, was established. The variance analysis was used to test the fitting degree of the model. The results showed that the regression model can accurately reflect the change relationship between the influencing factors and response values, and that it is well-fitted to the actual situation. Figure 11: Variation curve of pile-soil stress ratio before and after response surface optimization. (6) The optimal parameter combination of the maximum pile-soil stress ratio was obtained by establishing a multiple regression equation. The numerical simulation results showed that the pile-soil stress ratio increased by 13.4%. In summary, in this paper, a load transfer analysis method of embankments, considering the combined action of multiple factors, was proposed, to accurately calculate the pile-soil stress ratio under the embankment load. The change of embankment filling properties and geogrid strength will affect the degree of the soil arching effect and membrane effect, and the transfer efficiency of the soil arching effect and membrane effect on load is different. Therefore, in the design of pile-supported embankments, the reinforcement form of embankments should be determined first, and then the nature of embankment fillers should be determined to ensure that the design has a high load transfer efficiency. Writing--original draft preparation, X.W. ([PERSON]); writing--review, X.W. ([PERSON]); funding acquisition, G.Y. ; validation, Y.Z. All authors have read and agreed to the published version of the manuscript.