# A New Method for Evaluating the Bearing Capacity of the Bridge Pile Socketed in the Soft Rock
###### Abstract  
Aiming at the rock-socketed pile in the soft rock area, this paper studies the inherent constitutive relationship between the vertical restraint stiffness at the pier bottom and the bearing capacity of the pile foundation. A new method to evaluate the bearing capacity of the pile foundation is proposed. Based on the Rayleigh energy method and the Southwell frequency synthesis method, the analytical expression of the vertical vibration fundamental frequency of the pier was calculated, and the constraint stiffness expression of the pier bottom was derived. By investigating the impact of parameters on the bearing capacity coefficient of the pile foundation, the fitting formula of the bearing capacity coefficient was obtained by multiple linear regression. Then, with this method, the vertical fundamental frequency of the pier was obtained through a field dynamic test to calculate the vertical constraint stiffness and evaluate the bearing capacity of the rock-socketed pile in the soft rock area. This method can overcome the shortcomings of the traditional static load test method, such as the high cost, long cycle, and poor representativeness. Finally, this method's accuracy was verified by comparing field measurements and finite element simulation results. The results show that the difference between the code design constraint stiffness and the constraint stiffness by the frequency synthesis method was about 0.7%, and the bearing capacity difference between the analytical solution and the numerical simulation was small. The new method is accurate and effective. rock-socketed pile; soft rock; frequency synthesis method; multiple nonlinear regression; restraint stiffness; bearing capacity coefficient +
Footnote †: journal: Applied Sciences  
19 June 2021  
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embedded depth and section roughness [13]. By considering the elastic and elastic-visco-plastic properties of the surrounding and underlying soils, [PERSON] et al. [14] presented a method for determining an incompressible pile's settlement and bearing capacity. [PERSON] et al. [15] investigated the bearing mechanism of rock-inclined piles and proposed an efficient method to estimate the bearing capacity of the piles. Due to the large bearing capacity and high cost of a static load test of the rock-sockeded pile in weak rock, almost no destructive tests have been carried out in engineering applications. Therefore, the research on the bearing properties of rock-socked piles in the soft rock area is mainly based on modeling tests. The vertical bearing capacity of rock-socked piles is generally obtained by numerical simulation and field test piles measured data [16; 17; 18]. [PERSON] et al. [19] conducted indoor model tests of rock-socked piles in the soft rock under different overburden pressures and socketed depths, investigated the piles' axial bearing characteristics, and revealed the bearing mechanism and influencing factors. To obtain the natural frequency calculation of structures, researchers [20; 21; 22; 23] have investigated different methods. The frequency synthesis method is an effective way to establish the relationship between the natural frequency and the constraint stiffness. With the frequency synthesis method, [PERSON] and [PERSON] deduced the natural frequency of the variable cross-section pier, considering the support spring constraint and proposed the analytical algorithm of the transverse vibration frequency of the column pier [24]. [PERSON] et al. studied the bridge pile foundation vertical capacities based on numerical simulation and indoor model tests, analyzed the relationship between the position of the pile and the resistance of the pile side and the bearing capacity of the pile foundation, and proposed a more accurate indoor pile foundation test method [25].