## 4 Materials and Methods
### Developing the Model
#### 4.1.8 Mesh Generation and Calibration  
To create a suitable mesh for static and dynamic testing, a brick element is required to create a three-dimensional model. ABAQUS has two standard brick elements, an eight-node linear brick, (C3D8) and an eight-node linear brick with reduced integration and automatic hourglass control (C3D8R). The C3D8 element consists of \(2\times 2\times 2\) integration points, whilst C3D8R element consists of one central integration point as shown below in Figure 8.  
As the C3D8 element undergoes full integration, the element does not respond well to plastic deformation [36]. Therefore, as the double shear test model investigates plastic deformation of both the bolt under investigation and the concrete encasing, C3D8R elements will be utilised. It should be noted that the integration point is in the centre of the element, thus finer elements are required to display accurate stress concentrations at the boundary of the geometry. The finer a mesh becomes, the greater the computational time, thus a fine mesh will only be utilised in areas of interest. ABAQUS has an automatic meshing feature which creates a basic mesh when an element seeding size is nominated. To enhance this feature and create a more favourable mesh, manual localised subdivisions are created in individual parts in critical areas including contact regions and areas experiencing large deformation and stress concentrations. Additionally, by creating manual partitions, mesh size in critical areas can be varied without using mesh grading, avoiding irregularly shaped elements. This was applied to the cable bolt and concrete box. The cable bolt shown in Figure 9, demonstrates the effects of manual partitioning prior to auto-meshing compared with no partitions. The mesh size of the concrete surrounding the bolt was fine, while maintaining a coarse mesh in areas of little interest, as demonstrated below in Figure 10.  
Figure 8: Geometry and integration of brick elements (**a**) C3D8 and (**b**) C3D8R. Figure 9: Cross section of steel bolt mesh optimisation. As the two boundary blocks of concrete are fixed, the area of interest of the bolt is the region of the bolt encased by the centre block. In addition to the central third of the bolt, the finer mesh was also extended to the 50 mm gaps where the bolt was not encased in concrete. The fine mesh was made twice as fine as the remainder of the bolt, as shown below in Figure 11.  
To utilise the automatic mesh function, element seeding sizes must be defined in the X, Y and Z planes. Therefore, to mesh the sphere for dynamic tests, manual partitions were created in all three planes such that seeding size could be defined. The meshed sphere is shown below in Figure 12.  
Once all geometric parts were individually meshed, the assembled static and dynamic model meshes were generated, as shown below in Figure 13.  
Figure 11: Fine bolt mesh. Figure 12: Load sphere mesh. Figure 10: Cross section of concrete box mesh optimization. To determine the exact element seeding size to produce an optimised mesh such that accurate results with minimal computational time were achieved, varying fine mesh sizes were tested against the experimental data, as shown below in Figure 10.0 A seeding size of 10, 15, 20 and 25% of the bolt's diameter was tested for the finer central section of the steel bolt where the remainder of the bolt's mesh was assigned as double the seeding size of the fine mesh. The concrete in contact with the entirety of the bolt was assigned the same seeding size of the bolt's finest mesh. Furthermore, the maximum shear force and computational time for each fine mesh has been summarised in Figure 10.1 Computational times of different fine meshes in static testing. All fine meshes that were tested displayed a similar trend to the experimental data within reason. As the mesh became coarser, the computational time decreased significantly, however the maximum shear force became less accurate as the C3D8R elements were utilised.