# A New Method for Evaluating the Bearing Capacity of the Bridge Pile Socketed in the Soft Rock
## 3 Field Test and Numerical Simulation
### Finite Element Numerical Simulation  
The actual structure was simplified to an axisymmetric finite element model for simulation. The finite element model of the test pile and rock-soil stratum was established by ABAQUS, and the CAX4R element (a 4-node bilinear axisymmetric quadrilateral, reduced integration, hourglass control) was used to simulate the pile and rock-soil stratum. In order to ensure the accuracy of the analysis and the efficiency of the calculation, the finite element mesh of the rock mass was divided into near pile and far pile. The model boundary conditions were set as follows. On the surface of the rock and the soil mass and cap, a free boundary was set. Then, after reaching a certain range of bedrock, the displacement of the pile top load was almost zero, so the surface was under the fixed displacement constraints. The lateral soil adopted horizontal displacement of the fixed constraints, and the vertical displacement of the free development of the pile side used the axial symmetry constraint. The pile bottom and rock mass were connected by Tie to achieve displacement coordination. The linear elastic constitutive model was used for the concrete pile, as the Mohr-Coulomb model is an ideal elastic-plastic model that can consider the influence of the stress state and stress history on the rock and soil and better simulate the nonlinear and dilatancy of the rock and soil. It was used for the rock-soil stratum. The contact pair algorithm was used to simulate the contact surfaces, as it can simulate the fracture, slip, and dislocation between the pile and soil-rock stratum. The normal behavior of the contact surfaces used the hard contact model. The pile and the rock-soil stratum can transfer normal pressure under the compression state, and the amplitude of the pressure is not limited. When there is a gap, the normal pressure is not transferred. The tangential behavior of contact surfaces used the friction model.  
The initial equilibrium state of the pile rock-soil stratum system was established by the automatic ground stress balance step. Figure 7a,b show the distributions of stress and displacement before the initial stress equilibrium. Figure 7c,d show the distributions of stress and displacement after the initial stress equilibrium. Through comparison, it can be seen that the magnitude of stress remained unchanged after the stress equilibrium, and the magnitude of maximum displacement was \(1\times 10^{-16}\) (m). Thus, the results of the initial ground stress equilibrium are precise enough for the finite element simulation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Density \(\rho\) & 2549 & kg/m\({}^{3}\) \\ Elastic modulus \(E\) & \(3.25\times 10^{10}\) & \(MPa\) \\ Vertical fundamental frequency \(\omega_{v}\) & 23.66 & \(Hz\) \\ Mass of the pier top \(M\) & 82,913.87 & \(kg\) \\ Mass of the pier cap \(m_{c}\) & 39,941.62 & \(kg\) \\ Mass of the pier \(m_{d}\) & 73,513.90 & \(kg\) \\ Pier height \(H\) & 9.4 & \(m\) \\ Cross-section diameter \(D\) & 1.5 & \(m\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The test pier material’s design parameters.