# An Improvement of the Load Transfer Method for Energy Piles Under Thermo-Mechanical Loads
## 2 Materials and Methods
### Improvement of Load Transfer Method for Energy Piles
#### 2.3.3 Improve the Method  
It has been mentioned above that the calculated results of the load transfer method established by [PERSON] (15) (2011) applied to the study of energy piles showed large deviations between the calculated axial force values at the top of the pile and the actual loading. After analysis, it is known that this is caused by using \((\sum Q_{T}^{NP})_{\text{min}}\) instead of \((\sum Q_{T}^{NP})=0\) in determining the neutral surface. Although this method can determine the approximate location of the neutral plane, it also brings a large error to the calculation results of the pile top, which can be recorded as the pile top unbalance force. The iterative algorithm for pile top unbalance force elimination established in this paper can well solve the pile top error brought by the above problem, and the specific steps are as follows.  
Step 1: The approximate location of the neutral surface is determined according to the algorithm shown in Figure 2.  
Step 2: The distribution of the axial force, strain, and lateral resistance of the energy pile along the pile is determined according to the algorithm shown in Figure 4.  
Step 3: The value of the loading at the top of the pile is known and is denoted as P. The calculated axial force at the top of the pile is denoted as \(\sum Q_{\text{top},T}^{1}\). The difference between them is calculated as the unbalanced force at the top of the pile.  
Step 4: The unbalanced force at the top of the pile obtained from the calculation is added back to the top of the pile, and the axial force, strain, and displacement due to the unbalanced force are obtained using the load transfer method.  
Step 5: The axial forces, strains, and displacements due to unbalanced forces are superimposed on the results calculated by the algorithms shown in Figures 2 and 4, thus updating the results of the axial force, strain, and displacement distribution of the pile.  
The flow chart of the iterative algorithm for the unbalanced force at the top of the pile is shown below.  
The test conditions shown in Figure 6 were calculated and analyzed according to the iterative algorithm for the elimination of the unbalanced forces at the top of the pile. The calculated results were also compared with the results of the load transfer method established by [PERSON], the test results, and the matrix displacement method constructed by [PERSON] et al. (22), as shown in Figure 7. It can be found that the axial force at the top of the pile calculated by the improved method is consistent with the value of the actual loading at the top of the pile, and the results of the axial force and lateral resistance distribution along the pile body obtained by the method are consistent with the pattern of the experimental values, and the results are similar, which can better reflect the effect of thermo- mechanical coupling on the performance of energy piles.  
Figure 6: Iterative algorithm for eliminating unbalanced force on the top of the pile (Tips: K\({}_{0}\) is the stiffness of the pile at the top).