## 1 Introduction  
In order to ensure the safety and reliability of pile foundations, the bearing capacity test of the pile foundation is essential [1, 2, 3]. The traditional methods for static load testing of foundation piles mainly include the vertical compressive pile load method and anchor pile method [4, 5, 6, 7], the high-strain method for dynamic testing of pile bearing capacity [8, 9], the probability analysis model, which predicts and evaluates the accuracy of the single-pile bearing capacity [10, 11, 12], and the finite element approach of numerical simulation of the pile foundation [13, 14, 15]. However, a novel technique for evaluating the bearing capability of foundation piles is the self-balanced test pile method. There is no requirement for a pressure platform or anchor pile reaction device, in contrast to the conventional stacking method and the anchor pile method. It is frequently used in practical engineering to establish the final bearing of a single pile, since it can save testing time, labor costs, and manpower requirements [16, 17]. [PERSON] first tested the monopile bearing capacity usingself-balanced test piles in 1989, which has since then been widely used in several parts of the world [18; 19; 20]. Furthermore, several specifications have been developed for it [21; 22; 23; 24]. A major difficulty in the promotion and use of this technology is how to translate the test findings of the self-balanced approach into results that are comparable to standard static load tests. Based on [PERSON]'s displacement solution, [PERSON] et al. proposed a method for the calculation of loads in piles, a technique that takes into account the resistance of the connecting shaft [25; 26]. [PERSON] et al. studied the load action law of self-balanced piles, considering, among others, the residual load distribution, and evaluated the displacement variables of prestressed, high-strength concrete piles in deeper foundations [27]. The numerical method was utilized by [PERSON] et al. to determine the conversion coefficients, variation laws, and soil elastic modulus for various length-to-diameter ratios [28]. The properties of the self-balanced pile load transfer function are the main focus of many scholars' study findings, but the conversion method has not been examined [29; 30; 31]. Currently, in engineering, the test results of self-balanced test piles are converted to conventional static load test \(\mathbf{Q}\)-\(\mathbf{s}\) curves by the exact conversion method and the simplified conversion method. With the simple conversion method, it is difficult to determine the exact value of the conversion coefficient in different soil layers [23; 24; 32], and it lacks of some theoretical support [33; 34; 35]. The precise conversion method also increases the burden on the test pile, since each micro-segment's displacement and internal force need to be measured with many specific displacement transducers [36]. Therefore, there is still room for improvement on the self-balanced theory within the current study. In order to calculate the ultimate bearing capacity of a single pile more accurately, it is essential to research the load transfer mechanism in the test pile of the self-balanced method and find a suitable theoretical analytical conversion method. According to the self-balanced loading model, the displacements generated by the upper and lower piles interact with each other under the action of the load box. The skin friction resistance of the pile produces additional stress on the pile end, which causes additional settlement at the bottom of the lower pile. The additional settlement affects the relative displacement of the pile soil of the upper pile [37]. As a result, [PERSON]'s solution was employed in this study to determine the additional pile bottom settling brought on by the side friction resistance of the top pile [28]. In addition, it is considered that the load action function follows the Kraft model when taking into account the impact of the top pile's weight on the ability to resist loading.