# Comparison of Prediction Methods for Axial Strength of Ground Connections with Shear Keys
## 4 Comparison between Calculation and Test Results
### Data Acquisition and Verification
Abaqus was selected for finite element simulation analysis. It is particularly significant to select the appropriate material models of compression and tensile properties of the grouting body. Given that the grouting material is a nonlinear brittle material, the concrete damage plastic (CDP) model was chosen for the simulation, which can effectively reflect the main failure mechanism of the brittle material. The basic model parameters of the material are shown in Table 4. For the steel, the elastoplastic material model based on classic metal plasticity theory was adopted in Abaqus. The [PERSON] yield criterion and kinematic hardening theory were used. The elastoplastic strengthening model of the ideal double-fold line was adopted for the constitutive relationship of the steel in this paper. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Young’s** & **Yield Strength** & **Ultimate** & \multirow{2}{*}{**Poisson’s Ratio**} \\  & **Modulus (MPa)** & **(MPa)** & **Strength (MPa)** & \\ \hline Steel & \(2.06\times 10^{5}\) & 380 & 565 & 0.31 \\ Grout (GC-S75) & \(5.1\times 10^{4}\) & / & 149.1 & 0.2 \\ Grout (GC-S50) & \(5.1\times 10^{4}\) & / & 149.3 & 0.2 \\ Grout (GC-S100) & \(5.1\times 10^{4}\) & / & 154.2 & 0.2 \\ Grout (GC-H2.5) & \(5.1\times 10^{4}\) & / & 150.2 & 0.2 \\ Grout (GC-N2) & \(5.1\times 10^{4}\) & / & 131.2 & 0.2 \\ Grout (GC-T38) & \(5.1\times 10^{4}\) & / & 150.2 & 0.2 \\ Grout (GC-T63) & \(5.1\times 10^{4}\) & / & 150.3 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Material properties. Figure 10: Arrangement of (**a**) displacement transducers (DTs) and (**b**) strain gauges on specimens. The outer casing tube, steel pipe pile, and grouting section of the grouting connection were modeled with 3D solids, and the unit was an eight-node hexahedral linear reduction integration unit (C3D8R). The modeling method was the axisymmetric semi-structural method. The contact setting included the contact of the steel casing with the grouting material and the contact of the grouting material with the steel pipe pile. Surface contact was established between the grouting material and the inner wall of the steel casing and the outer wall of the steel pipe pile. Between the grout and the steel pipe interface, a contact pair was set up for face-to-face contact. The contact in the normal direction was set as a hard contact, and a Coulomb friction model with a penalty function was used in the tangential direction. The model friction coefficient was taken as 0.4. A fixed constraint was imposed on the top surface of the steel pipe pile. Due to the use of axisymmetric semi-structure modeling, the symmetry constraint was imposed on the axisymmetric cross-section of the grouting connection specimen. The center of the axis of symmetry of the steel casing was selected to set a reference point, the reference point was coupled to the bottom surface of the outer sleeve, and a displacement load was applied to this reference point. The model boundary conditions are shown in Figure 11.  
The test results were fitted by continuously adjusting the characteristic parameters of the finite element model, focusing on the load-displacement curve and failure mode as the data fitting target. A comparison table of the ultimate strength (Table 5), a comparison diagram of the load-displacement curve (Figure 12), and a comparison diagram of the final failure mode (Figure 13) were obtained after the fitting study. The calculated results of the fitted finite element model agree with the test results. The main factors affecting the finite element model are the material model parameters of the grout. The values of specific parameters are shown in Table 6.  
Figure 12: Comparison of test load–displacement curves: (**a**) S75; (**b**) S50; (**c**) S100; (**d**) H2.5; (**e**) T38; (**f**) T63; (**g**) N2. A finite element analysis of 51 specimens in the database was performed using the fitted model parameters obtained from the experiments.