## 3 Results and Discussion
### Model Results, Comparison and Discussion
#### 3.5.3 Discussion of Numerical Model Design  
Confirmation of sufficient meshing sizes was not possible with standard convergence studies due to the appearance of hot spots likely caused by contact singularity. Even with geometric refinement and the inclusion of 0.25 mm fillets, meshing studies did not converge. However, when looking at the overall stress distribution and strain response in the centre of  
Figure 16: Comparison of model performance: (**A**) 2D model [18], (**B**) 3D contact model. the specimen, confidence in both the meshing and geometrical simplification was achieved. The comparison of stress between the two models can be seen in Figure 18. Furthermore, as the main objective was the strain response, this was also compared between the two models; the largest difference between them was found to be 3%. To confirm this sufficient meshing with the larger models, an additional second verification was conducted. The 250 mm and 750 mm of the alternated bars were both investigated. For the 250 mm between the coarse and finer (117 k to 147 k nodes), there was a 0.16% difference in deflection, with the 750 mm having a similar level of consistency. Another important factor for investigation is the contact normal stiffness factor. Generally, with increased normal stiffness the penetration will decrease, while contact pressure, stress and iterations to solve will increase. Values were selected by conducting convergence studies, with the first-stage models being 10 for the pipe grout contact and 3 for the grout rebar contact; however, this was increased to 15 for the pipe grout contact. Convergence models were generally in line with the stated expected response. However, in the first-stage model, maximum stress in other bodies (not the ones found at the contact interface) decreased with increased rebar-grout contact pressure, and the pipe grout seemed to peak at a normal stiffness factor of 10. These selected values are in line with expected contact behaviour where the pipe-grout is bonded and the grout rebar is frictional. To ensure boundary and load conditions were properly represented, investigation into their response and effects on results was explored. The application of load was very closely represented to the laboratory condition, in the laboratory loading was achieved with a hydraulic grip \(\sim\)20 cm from the front of the pipe and in the numerical model this was represented as the load was applied across the entire surface area of the front of the rebar in the numerical model. To keep the model efficient, the bearing plate used to hold the specimen in place was represented by a boundary condition that was applied across the top face of the pipe to constrain the X (plane of loading). The Y component was constrained by the plane of symmetry of the model. In the laboratory, specimens were restrained in the Z and Y by the friction between the pipe and the bearing plate. This could be represented as an additional friction contact surface. To simplify this, a plane of  
Figure 17: Strain attention of various rib spacings at 10 and 50 kN (stage 2.1 and 3.1 models). symmetry was created on the pipe and the Z was constrained on the edge which would interface with the pipe. The boundary conditions created slightly less confinement on the top of the pipe than the actual specimen, but was selected this way with consideration that the frictional force would be proportional to the applied load and with expected grout conical failure, very little force would be transferred in this region. When analyzing the load response of 20 kN of loading, the X boundary condition reaction forces were directly equal to the applied load. Reactionary forces in the other planes at the X and Z boundary condition were either small (-4% and -2%) or zero. These results were in line with the expected response of the system. To understand the effects of making the model freer than the physical testing, another model was run but with the entire face of the pipe constrained in all directions.