## 1 Introduction  
Uplift piles are widely used in the anti-floating of underground engineering, anti-uplift of tower foundations of power transmission and transformation engineering, anti-uplift of tower foundation for communication, anti-uplift of high-rise chimney foundation, anti-wind and a wave of offshore platform and other projects. Due to its extensive engineering application, it has aroused interest in research [1; 2; 3; 4; 5]. [PERSON] et al. [6] concluded from model tests that the loading capacity of the uplift pile increases with increasing pile embedment ratio and increasing sand compactness. For dense sandy soils, the load-displacement curve of the uplift resistant pile is a straight line segment before the peak load. [PERSON] et al. [7] proposed the construction method of the load-displacement curve of uplift piles according to the load transfer curve between the pile-soil interface, where the development of shear stress at the pile-soil interface affects the shape of the load-transfer curve, and also considers the effect of Poisson's ratio and stress relaxation of the pile on the pile bearing capacity. [PERSON] et al. [8] found that before the critical embedment ratio of the pile, the unit shaft resistance increased linearly with the pile length, and the critical embedment ratio of the pile was related to the relative density of the soil. Based on the laboratory test, the estimation formula of the ultimate uplift bearing capacity was proposed. According to [PERSON] [9], the uplift shaft resistance of piles under axial load can be expressed by the uplift coefficient. In sandy soil or clay, the greater the inclination of anchor piles, the greater the uplift coefficient of piles. With the increase of the embedment depth of piles, the influence of the inclination of piles on the uplift bearing capacity is weakened. For uplift piles with a given burial depth, when the inclination of piles is less than 45\({}^{\circ}\), the change of the shaft resistance with the pile inclination is not obvious. [PERSON] et al. [10] proposed a method for calculating the loading capacity of uplift resistant piles in sandy soils. The influence of the length of the pile, the diameter of the pile, the surface characteristicsof the pile, and the soil properties on the bearing capacity can also be considered, and the critical embedment depth of the pile is not only related to the density of the soil, but also to the soil properties. [PERSON] et al. [PERSON] et al. (2018) established a formula for calculating the bearing capacity of the uplift pile anchor based on [PERSON]'s formula, which can directly calculate the bearing capacity of the uplift pile without reference to a specific chart, and compared with 28 cases, the predicted results of this method are in good agreement with the case results. According to different failure surfaces of the soil around piles, [PERSON] (1967), [PERSON] et al. [PERSON] et al. (2018), and [PERSON] et al. [PERSON] et al. (2018) proposed formulas to calculate the net bearing capacity of uplift piles with similar principles. It is well known that uplift piles have lower bearing capacity than compressive piles, but there are different understandings of its causes. [PERSON] et al. [PERSON] et al. (2018) used digital image correlation (DIC) techniques to model piles with different roughness of the pile surface in sandy soils to obtain displacement and strain fields in sandy soils. The data from DIC showed that the magnitude of the pile surface roughness was related to the shaft resistance and the displacement and strain fields in the soil on the pile side. The greater the pile surface roughness, the greater the pile shaft resistance, and the greater the displacement and strain in the soil. [PERSON] et al. [PERSON] et al. (2018) considered that the method of using the shaft resistance correction coefficient of the compression pile to obtain the shaft resistance of the uplift pile is limited.